Question

The radius of the circle passing through the foci of the ellipse (x²/16) + (y²/9) = 1 and having its centre (0, 3) is ........

(a) 4

(b) 3

(c) √12

(d) (7/2)

Answer 1

The correct option (a) 4  

Explanation:

ellipse is (x²/16) + (y²/9) = 1

here    a² = 16  and     b² = 9.

Now    b² = a²(1 – e²) ⇒ (9/16) = 1 – e² 

⇒ e² = 1 – (9/16) = (7/16)

∴   e = ± (√7/4)

∴ Foci are (√7, 0) and (– √7, 0).

Centre of circle is at (0, 3) and it passes through radius of circle

√[(√7, 0)² – (0, 3)²] = √(7 + 9) = 4.