Intercept of a Line or Length of a Chord

There are few things which student should know when dealing with online quiz. Here are some shortcuts which can lead to success.The length of a chord AB of a circle (or the intercept made by a circle on a line) is given by

AB=2√a^2-p^2

Where ‘a’ is a radius of the circle and ‘p’ is the length of the perpendicular from its centre on the chord. In particular the circle x^2+y^2+2gx+2fy+c=0 cuts

i. Intercept on x-axis=2√g^2-c

ii. Intercept on y-axis=2√f^2-c

EX: Find the length of intercept on y-axis, by a circle whose diameter is the line joining the point

(-4, 3) and (12,-1)

Solution: Here the equation of the circle (x+4) (x-12) + (y-3) (y+1) = 0

Or x^2+y^2-8x-2y-51=0

Here intercept on y-axis

= 2√f^2-c

=2√1-(-51)

=4√13

POSITION OF A POINT AND LINE WITH RESPECT TO A CIRCLE

Position of a point

A point (x, y) lies outside, on or inside a circle S= x^2 + y^2 + 2gx + 2fy + c = 0 according as

S=x^2 + 2gx + 2fy + c is positive, zero or negative. So

•  S > 0 =(x , y) is outside the circle 
•  S > 0 = (x , y) is on the circle 
•  S > 0 = (x , y) is inside the circle 

Position of a line 

Let L=0 be a line and S=0 be a circle. If ‘a’ be the radius of the circle and ‘p’ be the length of the perpendicular from its centre on the line, the

•  p > a = line is outside the circle 
•  p = a = line touches the circle 
•  p < a = line is a chord of the circle 
•  p = 0 = line is a diameter of the circle 

Tutor Pace.com - Innovative Online Tutoring Services

Tutor Pace Inc, Texas based online tutoring company offers myriad innovative online tutoring services round the clock allow students to get the help they really in need of it. It is fabulous option that adds additional enrichment to your child's academic growth. It offers innovative study programs from experiences tutors that help students learn in a systematic and effective manner. They start loving the subjects by mastering concepts.

Live On-Demand Tutoring:

Tutor Pace offers on demand tutoring anywhere and anytime wanted. The students remain connected one-on-one with the tutor with no wait time. It offers flexibility that suit schedule of every student.

Scheduled Based Tutoring:

Tutor Pace allows to book pre-schedule session as per the convenience of the students. The sessions can be booked on daily or weekly recurrence which saves time for other task to complete.

Session Replay:

The sessions conducted online are recorded are made available to students to access and replay for studying or revising lessons/topics of various subjects. This is very useful especially at the time of test preparation.

Tutor Pace Inc. serves thousands of students with great satisfaction that lead them to attain A+ grade in their academics. Lots of students take science and math tutor online help. Online math tutor offer not only give homework help but live tutoring through the lessons. Try out free online tutoring on the subject of your difficulties.

How Tutor Pace Works as Trusted Online Tutoring Website?

Lot of online tutoring websites are influencing students to take lessons online, but they all may not be offering trusted online tutoring. You need to ensure twice about tutoring program is being perceived as cheating or plagiarism. Tutor Pace is one of the most trusted sites in online tutoring which offers guarantee towards improving grade to A+.

As first step towards trusted online learning, Tutor Pace offers Demo session with free online tutor who are experienced and qualified one. It helps to gain understanding of how online personalized tutoring works. Tutor Pace offers the same quality of regular tutoring as given in demo session. Students can try out free online Math tutor in demo session.

The students are collaborated with tutor online in a secured online classroom equipped with live chat and two-way interactive whiteboard. The sessions recorded for future use of the students is kept strictly confidential.

Often tutors gave their username and password to some another person who can take tutoring. Typically, this happens with tutors taking lower grades tutoring where anybody can teach students of elementary grade. Tutor Pace follows stringent rules and regulations stopping such kind of activities. It has laid down rules and regulations to take action punishing the act of cheating.

Lots of tutoring websites work on homework, assignments on behalf of students. This is wrong practice. Tutor Pace does not support such kind of assistance or support. The tutor and student take collaborative tutoring session working on regular tutoring, homework, assignments and test preparation. The online tutors at Tutor Pace analyze student’s weak areas in the subject/topic and work towards providing focused one-to-one individualized tutoring.

Tutor Pace does not practice promotion with false advertisements. We do mean for each of the features we give to our tutors, students and parents. We do not catch hold students with false commitment. Tutor Pace mission is to offer outstanding guidance and affordable education to our students round the clock through sophisticated online tutoring system. Tutor Pace means for each word that describes it’s mission statement. May it be quality tutoring or pricing factor, we are transparent enough to all our clients.

Tutor Pace Inc., Texas based company offers Texas State Law accredited online tutoring services is gaining its popularity as one of the most trusted site in its business.

Some Important Definition and Facts about Geometry

Some definitions students should know as they make basic concept and these are regularly asked in online classes. Let’s see some of them.

A circle is the locus of a point which moves in such a way that its distance from a fixed point is constant. The fixed point is called the centre of the circle and the constant distance is called the radius of the circle.

Tangents and Normal’s

Definition by Tutor Online:

A tangent to a curve at a point is defined as the limiting positions of a secant obtained by joining the given point to another point in vicinity on the curve as the scond point tends to the first point along the curve or as the limiting position of a secant obtained by joining two points on the curve in the vicinity of the given point as both the points tend to the given point.

Two tangents, real or imaginary, can be drawn to a circle from a point in the plane. The tangents are real and distinct if the point is outside the circle, real and coincident if the point is on the circle and imaginary if the point is inside the circle.

The normal to a curve at a point is defined and the straight line passing through the point and perpendicular to the tangent at the point. In case of a circle every normal passes through the centre of the circle.

Chord of Contact:

From a point P(x, y) two tangents PA and PB can be drawn to the circle. The chord AB joining the points of contact A and B of the tangents from P is called the chord of contact of P(x, y) with respect to the circle.

Boost your Calculus understanding with Online Tutoring

The academic burden of children gradually grows as they grow with age. It is essential that your child becomes capable enough to resist that change and accept the burden with increased learning capabilities. The level of studies starts becoming difficult as they reach higher grades. In this situation, often children start lacking to grasp Math concepts and formulae. Calculus, Trigonometry, Probability, Statistics are vast and difficult Math topics where children seek some extra tutoring. Online Math tutor works best in this situation.

Calculus is a virtual branch of Mathematics shows their links in the field of Engineering and Science. If your child learns formulae and solve the problem is not enough but it requires grasping Calculus conceptually. Math tutor online offers one-to-one individualized tutoring. The tutors identify difficult areas of understanding the subject and focus to boost up their understanding. Calculus tutoring explains the fundamentals and concepts by giving examples of situations happening in day-to-day lives. Online tutors employee interesting and interactive ways to make your child grasp fundamentals of Calculus in the way that they do not forget them easily. The Calculus concepts are well-built that your child becomes confident enough to apply those in day-to-day life.

It is sure that the Math tutoring online will make your children very handy in Calculus and not just restrict their intention of developing academic problem solving skills. There is no reason that stops you boosting Calculus understanding, ask for a free online tutoring session right now!

Tricky Proofs in Sine and Cosines asked in Online Test for 12th Grade USA Students

Online Math Tutoring - 

In any triangle ABC, prove that

1. A cosA + b cosB + c cosC = 4RsinA sinB sinC

2. sinA + sinB + sinC = S/R

Let’s see the solution of the following

1. lets first have left hand side equation which is
A cosA + b cosB + c cosC
= 2R sin A cosA + 2R sin B cos B + 2R sinC cos C

This is because as we know a = 2R sinA, b=2RsinB, c = 2RsinC

So now taking R common and converting into formula that is 2 sin A cosA = sin2A

= R (sin2A + sin2B + sin2C)

Again by applying formula

= R (2sin (A+B) cos(A-B) + 2 sinC cos C )

= R (2sin (π –C)cos(A-B)+ 2 sinC cos C )

= R (2sinC cos(A-B)+ 2 sinC cos C )

Now taking 2 sin C as common we have

= 2RsinC (cos(A-B)+ cos C )

= 2RsinC (cos(A-B)+ cos(π – (A+B ))

= 2RsinC (cos(A-B)- cos (A+B ))

= 2RsinC (2sinA sin B)

= 4R sin A sin B sin C = right hand side

Hence proved

2. sinA + sinB + sinC = S/R

here we should know things like

R = a/2sinA= b/2sinB = c/2sinC

sinA = a/2R, sinB = b/2R, sinC= c/2R

Just by putting these values in left hand side we get

a/2R +b/2R+c/2R = a+b+c/2R = 2S/2R = S/R = right hand side

Hence proved.

Online Math Homework Help Related With Straight Line

There are certain questions related with the topic straight line where students get homework. These questions are regularly asked from the students and they stuck in them and try to ask from online tutoring. As an online tutor many questions are regularly asked which I will discuss right now. Lets have two known principle we should know.

If the straight line cuts x – axis at A and y- axis at B, then OA and OB are known as intercepts of the line an x axis and y axis respectively. 

The equation of a line parallel to x axis at a distance b from it is y = b

Lets have questions related to this

Question: Determine the equation of line through point (-4, -3) and parallel to x axis

Solution: here it is given that slope which is m is zero. And value of x1 = -4 and y1 = -3
Now to find the equation of the line we should know the standard form
Which is y - y1 = m (x - x1) by putting the above values
This implies y +3 = 0(x + 4)
Y + 3 = 0

Question: Find the equation of the line for which tan θ = ½, where θ is the inclination of the line and x – intercept equal to 4. 

Solution: here m= ½
So equation of the line is
Y – 0 = ½(x – 4) here line passes through (4 , 0)
After solving the equation we get
X – 2y – 4 = 0

Strengthen your Pre Calculus in High School Grade

Calculus is the most difficult branch of Math. Typically, the study of basics in Pre Calculus form the part of High school curriculum. Later in college study, the topic is taught more in detail. Calculus is used in varied fields like demography, medicine and science. Hence, the students who wish to take degree which comprises study of Calculus should build their foundation right from high school grade.

As the subject is challenging lot of students welcome extra help with calculus. There are various ways to get extra tutoring; however, online tutoring may give you good option to learn the subject with expert all across the world. If student spent regular time towards learning the concept and keep practicing then the subject is doable. 

Here are few tips from Calculus online tutors towards improving grades of the student:

• Do not skip attending Calculus class either in school or personal tutoring.
• Note taking would help to concentrate and give reference point at the time you study topic later. 
• Math is the subject of practicing and Calculus is no exception.
• High school students are learning Calculus for the first time should spend more time practicing solving problems.
• Working on worksheets, practicing questions improves your problem solving skills.
• More practice will give you an idea of what sort of questions are expected to be asked in tests.
• More practice will help you to solve problems quicker which ultimately saves time solving difficult questions while taking test.

These are just few tips towards making strong base of Pre Calculus. Math tutor online offer best guidance and help in building strong foundation of pre calculus. Ask demo tutoring from good reputed tutor website that helps you to decide taking Math help.

What Does Online Math Tutoring Offer?

Math tutoring is available in learning Math concepts at each grade level which forms the part of the academic curriculum. It provides Math homework help, work out assignments, learning problem solving techniques, a lot of practical work and test preparation. The Online Tutors apply unique fun-way teaching methodologies that not only give a clear understanding about the topics but make this complex and vast subject very interesting and easy to digest.

Online tutoring has offer following topics in Math subject:

Arithmetic:

It makes you learn a core arithmetic skill that forms an important foundation of topics like fractions, decimals, percentages and ratio.

Algebra:

Functions, Graphs, Sequence and Series

This topic deals with most basic introduction to functions and its various types. It covers most basic concept to more advanced functions that met in engineering, economics and the sciences.

Geometry and Vectors:

It includes an understanding of Geometry concepts that are met in physics, engineering, architecture and design. You can get excellent foundation of this subject with understanding the qualities of the circle, lines and cones as well as a thorough explanation of vectors.

Trigonometry:

The geometry and trigonometry theorems are explained meticulously through animation and extensive real life case study. You will learn various other concepts like sine, cosine, tangent and measurement of radians.

Differentiation:

You can learn a very important topic called differentiation that deals with day to day life. You will learn to differentiate logs, exponentials, sines, cosines with excellent reference material that relate to the application of knowledge.

Integration:

Online Math tutoring includes the learning of integration, reverse process of differentiation. You will learn standard integration techniques with wide range applications.

You can find tutors to learn very primitive Math concepts to an extend that forms the part of college grade math. A good online tutoring website is the best source of taking Math help.

Why You Should use Math Tutor Online?

With a simple and effective approach, Math online tutoring is gaining popularity. The study result shows that learning Math online is much better than learned in a traditional classroom.
Here are the reasons to take Math help of online tutoring:

• You can get extensive help on your school academics may it be tutoring, homework help, Math problem solving or assignment work. 
• Your daily homework problems will no longer be a source of worrying 
• Online Math tutors design personalized study program according to student’s capabilities 
• You will get focused attention to solve all your problems in individualized sessions 
• The teaching methodologies applied in the Math subject are apt to make you learn boring and tough subject like this 
• You can learn problem solving techniques for all kinds of Math problems. 
• The online tutor adopts several techniques to make you understand single Math concepts. 
• Visuals, 3D imaging and Interactive animations used while teaching Math concepts never fail to create esired interest in the subject. 
• Math tutoring through internet is always fun-based learning with lot Math games, puzzles, quizzes, etc. 
• Online tutoring websites will definitely improve scores in your school academics 
• Private tutoring is Math subject is always an expensive option than online tutoring 
• You will get complete and extensive support sitting right at your home conveniently at very affordable prices. 

Before you start taking Math sessions, tutoring website will conduct diagnostic tests to identify the strength and attitude towards the subject. The tutor assists students with planned programs to overcome student’s weaknesses and focus of the required skill building.

Tutoring Geometry: Tips to make learning easy

Math Geometry is easier subject than Algebra, Calculus, and Trigonometry. Here you go through the tips that will make subject easier than ever before.

§  Geometry games, songs, rhymes help kids to learn basic concepts of Geometry during elementary level.

§  The computer can really help learn geometry. It allows dynamic, interactive manipulation of diagrams where child can rotate, move, and stretch figure and observe how changing properties change the definition of diagrams. Online tutoring services use interactive whiteboard attached to the computer where both student and online tutor can perform drawing together.

§  Online tutoring use games, quizzes and mock tests to sharpen geometry. They offer various kinds of resources like problem worksheets to practice geometry learning and flashcard to remember formulas.

§  While tutoring Geometry, ask as many as justifications, informal proof and “why” questions. Solve as much as many problems you can. Do not give up tough problems, solve them as a challenge.

§  Learn geometry concepts by showing correct and incorrect diagrams representing in various ways. Ask student to distinguish correct and incorrect diagrams with informal proof. This will strengthen Geometry concepts.

§  Give practice to student by asking them to draw correct and incorrect diagrams. The practice can be like drawing parallels and unparalleled lines. Further ask students to draw parallelogram and quadrilateral that is not a parallelogram. It helps them to draw geometry diagrams by their own.

§  Help students to experiment, analyze and play with geometrical figures and ideas with manipulative and lots of diagrams. Tutoring Online helps lot in such experimenting using computer and software applications.

§  Ensure that student prepare notes of his own geometry definition and concepts with correct and incorrect examples.

What are three Representation Methods of Online Math Tutoring ?

Probably, you could not recall how you learnt math multiplication say three times five makes fifteen. Yes, it was in too early days when you were studying in second or third grade. Recollecting those early days, you will find out there were three basic representation levels of Math tutoring.

Research says that human beings represent learning in basic three ways: 

Concrete Representation:

Concrete representation is performing an action on the object/s. Student use hands-on manipulative to arrive at the result. 

Let us take an example:

Consider 3 piles of 5 blocks. How many total blocks are there in all?

The online Math tutoring solve this problem with concrete representation. The tutor actually make 3  piles of 5 blocks and make student count each block to arrive at the solution. This method of learning Math is used for kindergarten or first grade student.

Pictorial Representation:

Pictorial representation is very common way as lots of elementary textbooks follow this method. Even the assignment or homework can be given to complete the picture of said example. Here the student can draw missing blocks as said in the problem and count each of them to arrive at the solution.

Symbolic Representation:

Math Tutoring Online is carried out in higher grade when the student gets enough mature understanding problem type and its solution with above to two representation methods. The student directly arrive at the solution representing Math multiplication symbolically as 3 * 5 = 15.

Maths tutoring online gives excellent learning involving students in lots of activities that use a combination of these three representation methods.