Processing math: 100%

Subscribe to our YouTube channel for the latest videos, updates, and tips.


Centre of the Ellipse

We will discuss about the centre of the ellipse along with the examples.

The centre of a conic section is a point which bisects every chord passing through it.


Definition of the centre of the ellipse:

The mid-point of the line-segment joining the vertices of an ellipse is called its centre.

Suppose the equation of the ellipse be x2a2 + y2b2 = 1 then, from the above figure we observe that C is the mid-point of the line-segment AA', where A and A' are the two vertices. In case of the ellipse x2a2 + y2b2 = 1, every chord is bisected at C (0, 0).

Therefore, C is the centre of the ellipse and its co-ordinates are (0, 0).

Solved examples to find the centre of an ellipse:

1. Find the co-ordinates of the centre of the ellipse 3x2 + 2y2 - 6 = 0.

Solution:

The given equation of the ellipse is 3x2 + 2y2 - 6 = 0.

Now form the above equation we get,

3x2 + 2y2 - 6 = 0

⇒ 3x2 + 2y2 = 6

Now dividing both sides by 6, we get

x22 + y23 = 1 ………….. (i)

This equation is of the form x2a2 + y2b2 = 1 (a2 > b2).

Clearly, the centre of the ellipse (1) is at the origin.

Therefore, the co-ordinates of the centre of the ellipse 3x2 + 2y2 - 6 = 0 is (0, 0)

 

2. Find the co-ordinates of the centre the ellipse 5x2 + 9y2 - 10x + 90y + 185 = 0.

Solution:    

The given equation of the ellipse is 5x2 + 9y2 - 10x + 90y + 185 = 0.

Now form the above equation we get,

5x2 + 9y2 - 10x + 90y + 185 = 0

⇒ 5x2 - 10x + 5 + 9y2 + 90y + 225 + 185  - 5 - 225 = 0

⇒ 5(x2 - 2x + 1) + 9(y2 + 10y + 25) =  45

(x1)29 + (y+5)25 = 1

We know that the equation of the ellipse having centre at (α, β) and major and minor axes parallel to x and y-axes respectively is, (xα)2a2 + (yβ)2b2 = 1.

Now, comparing equation (x1)29 + (y+5)25 = 1 with equation (xα)2a2 + (yβ)2b2 = 1 we get,

α = 1, β = - 5, a2 = 9 ⇒ a = 3 and b2 = 5 ⇒ b = √5.

Therefore, the co-ordinates of its centre are (α, β) i.e., (1, - 5).

● The Ellipse





11 and 12 Grade Math 

From Centre of the Ellipse to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Expanded form of Decimal Fractions |How to Write a Decimal in Expanded

    May 07, 25 01:48 AM

    Expanded form of Decimal
    Decimal numbers can be expressed in expanded form using the place-value chart. In expanded form of decimal fractions we will learn how to read and write the decimal numbers. Note: When a decimal is mi…

    Read More

  2. Dividing Decimals Word Problems Worksheet | Answers |Decimals Division

    May 07, 25 01:33 AM

    Dividing Decimals Word Problems Worksheet
    In dividing decimals word problems worksheet we will get different types of problems on decimals division word problems, dividing a decimal by a whole number, dividing a decimals and dividing a decima…

    Read More

  3. How to Divide Decimals? | Dividing Decimals by Decimals | Examples

    May 06, 25 01:23 AM

    Dividing a Decimal by a Whole Number
    Dividing Decimals by Decimals I. Dividing a Decimal by a Whole Number: II. Dividing a Decimal by another Decimal: If the dividend and divisor are both decimal numbers, we multiply both the numbers by…

    Read More

  4. Multiplying Decimal by a Whole Number | Step-by-step Explanation|Video

    May 06, 25 12:01 AM

    Multiplying decimal by a whole number is just same like multiply as usual. How to multiply a decimal by a whole number? To multiply a decimal by a whole number follow the below steps

    Read More

  5. Word Problems on Decimals | Decimal Word Problems | Decimal Home Work

    May 05, 25 01:27 AM

    Word problems on decimals are solved here step by step. The product of two numbers is 42.63. If one number is 2.1, find the other. Solution: Product of two numbers = 42.63 One number = 2.1

    Read More