Question

Two parabolas with the same axis, focus of each being exterior to the other and the latus rectum being 4a & 4b. The locus of the middle points of the intercepts between the parabolas made on the lines parallel to the common axis is a

(a) straight line if a = b

(b) parallel if a ≠ b

(c) parabola for all a, b

(d) ellipse if b > a

Answer 1

Correct option (c) parabola for all a, b

Explanation:

 The equation of parabola can be taken as 

y² = 4a (x-k) & y²= –4b (x+k) 

A line parallel to the common axis is y = h