Question

Question 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).

Class X1 - Maths -Conic Sections Page 255

Answer 1

Major axis is along X -axis . Hence , equation of ellipse is in the form of
x²/a² + y²/b² = 1 .


now, According to question, ( 4, 3) and ( 6, 2) passing through ellipse hence, both of these will satisfy equation of ellipse .

when put point (4, 3) in equation
4²/a² + 3²/b² = 1
16/a² + 9/b² = 1 -------------(1)

when put point ( 6, 2)
6²/a² + 2²/b² = 1
36/a² + 4/b² = 1 ------------------(2)

solve equations (1) and (2)
take 4 × equation (1) - 9 × equation (2)
64/a² + 36/b² - 324/a² - 36/b² = 4 - 9
(64 - 324)/a² = -5
( - 260)/a² = -5
a² = 52 , put in equation (2)
36/a² + 4/b² = 1
36/52 + 4/b² = 1
4/b² = 1 - 36/52 = 16/52
b² = 14

hence, equation of ellipse
x²/52 + y²/13 = 1

Answer 2

Answer:

answer is x2/52+y2/13=1