Question

Question 19 Find the equation for the ellipse that satisfies the given conditions: Centre at (0, 0), major axis on the y-axis and passes through the points (3, 2) and (1, 6).

Class X1 - Maths -Conic Sections Page 255

Answer 1

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

according to question, (3, 2) and (1, 6) passing through ellipse .so, both of these points will satisfy equation of ellipse .

put ( 3, 2) in equation of ellipse ,
3²/b² + 2²/a² = 1
9/b² + 4/a² = 1 ------------(1)

put (1, 6) equation of ellipse,
1²/b² + 6²/a² = 1
1/b² + 36/a² = 1 ---------------(2)

now, solve equations (1) and (2) .
take 1 × equation (1) - 9 × equation (2),
9/b² + 4/a² - 9/b² - 324/a² = 1 - 9
(4 - 324)/a² = -8
-320/a² = -8
a² = 40, put it in equation (2),
1/b² + 36/40 = 1
1/b² = 1 - 9/10 = 1/10
b² = 10

hence, equation of ellipse is x²/10 + y²/40 = 1