Question
Class 11MathematicsConic Sections

Find the equation of the ellipse which passes through the point (–3, 1) and has eccentricity √2/5 with x-axis as its major axis and centre at the origin.

Verified Answer

Let x2/a2 +y2/b2 = 1 be the equation of the ellipse passing through the point (-3,1).

∴ we have 9/a2 + 1/b2 = 1

Or 9b2 + a2 = a2b2

Or 9b2(a2 - e2) + a2 = a2a2(1 - e2)   (Using b2 = a2(1 - e2)

Or a2 = 32/3

Again b2 = a2(1 - e2) = 32/3 (1 - 2/5) = 32/5 

∴ The required equation of the ellipse is x2/(32/3) + y2/(32+5) = 1

Or 3x2 + 5y2 = 32.