Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

Ellipse - Defination

Example 9

Ex 10.3, 1

Ex 10.3, 3

Ex 10.3, 5 Important

Ex 10.3, 2 Important

Ex 10.3, 4

Ex 10.3, 6

Ex 10.3, 9

Example 10 Important

Ex 10.3, 8

Ex 10.3, 7 Important

Ex 10.3, 10

Example, 11

Ex 10.3, 12 Important

Ex 10.3, 11 Important

Ex 10.3, 13

Ex 10.3, 14 Important

Ex 10.3, 15

Example 12 Important

Ex 10.3, 16 Important

Ex 10.3, 17

Ex 10.3, 18 Important

Example 13 Important

Ex 10.3, 19 Important

Ex 10.3, 20 You are here

Last updated at May 29, 2023 by Teachoo

Ex 10.3, 20 Find the equation for the ellipse that satisfies the given conditions: Major axis on the x-axis and passes through the points (4, 3) and (6, 2). Since Major axis is on the x-axis So required equation of ellipse is 𝒙^𝟐/𝒂^𝟐 + 𝒚^𝟐/𝒃^𝟐 = 1 Given that ellipse passes through point (4, 3) & (6, 2) Points (4, 3) & (6, 2) will satisfy the equation of ellipse Putting x = 4 & y = 3 in (1) 〖(4)〗^2/𝑎^2 + 〖(3)〗^2/𝑏^2 = 1 16/𝑎^2 + 9/𝑏^2 = 1 Putting x = 6 & y = 2 in (1) 〖(6)〗^2/𝑎^2 + 〖(2)〗^2/𝑏^2 = 1 36/𝑎^2 + 4/𝑏^2 = 1 From (3) 16/𝑎^2 = 1 − 9/𝑏^2 1/𝑎^2 = 1/16 (1 − 9/𝑏^2 ) Putting value of 1/𝑎^2 in (2) 36/𝑎^2 + 4/𝑏^2 = 1 36(1/𝑎^2 ) + 4/𝑏^2 = 1 36(1/16 (1−9/𝑏^2 )) + 4/𝑏^2 = 1 36/16 (1−9/𝑏^2 ) + 4/𝑏^2 = 1 9/4 (1−9/𝑏^2 ) + 4/𝑏^2 = 1 9/4 − 81/〖4𝑏〗^2 + 4/𝑏^2 = 1 (−81)/(4𝑏^2 ) + 4/𝑏^2 = 1 − 9/4 (−81 + 16)/(4𝑏^2 ) = (4 − 9)/4 (−65)/(4𝑏^2 ) = (−5)/4 (−5)/4 (13/𝑏^2 )= (−5)/4 13/𝑏^2 = 1 1/𝑏^2 = 1/13 b2 = 13 Putting value of b2 in 1/𝑎^2 = 1/16 (1 − 9/𝑏^2 ) 1/𝑎^2 = 1/16 (1 − 9/13) 1/𝑎^2 = 1/16 ( (13 − 9)/13) 1/𝑎^2 = 1/16 ( 4/13) 1/𝑎^2 = 1/52a a2 = 52 Equation of ellipse is 𝑥^2/𝑎^2 + 𝑦^2/𝑏^2 = 1 Putting value of a2 & b2 𝒙^𝟐/𝟓𝟐 + 𝒚^𝟐/𝟏𝟑 = 1