If the lengths of semi - major and semi - minor axes of an ellipse are 2 and √3 and their corresponding equations are y – 5 = 0 and x + 3 = 0, then write the equation of the ellipse.

Question

Philoid · Accepted Answer

Given that we need to find the equation of the ellipse whose semi - major and semi - minor axes are 2 and and their corresponding equations of equations of axes are y - 5 = 0 and x + 3 = 0.

We know that the centre is the point of intersection of both axes. So, on solving these axes we get the centre to be (- 3,5).

⇒ Semi - major axis(a) = 2

⇒ a² = 4

⇒ Semi - minor axis(b) =

⇒ b² = 3

We know that the equation of the ellipse whose centre is (p,q) and the length of semi - major axis is a and semi - minor axis is b is .

∴ The equation of the ellipse is .