Question

Find the equation of the ellipse referred to its major and minor axes as the coordinate axes x, y respectively with latus ** of length 4 and the distance between foci 4√2.

Answer 1

Let the equation of the ellipse is x2/a2 + y2/b2 = 1 (a > b)

Length of the latus ** = 2b2/a2 = 4 ⇒ b2 = 2a.

Foci are (ae, 0), ' (– ae, 0)

Distance between the foci = 2ae = 4√2

ae = 2√2

b2 = a2 (1 – e2) = a2 – (ae)2

2a = a2 – 8 ⇒ a2 – 2a – 8 = 0

(a – 4) (a + 2) = 0

a = 4 or – 2

a > 0 ⇒ a = 4

b2 = 2a = 2. 4 = 8

Equation of the ellipse is

x2/a2 + y2/b2 = 1

x2/16 + y2/8 = 1

x2 + 2y2 = 16