1.

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

Answer»

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

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

Foci are S (ae, 0), S' (– 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



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