Question

Let P be the parabola which is the locus of the midpoints of focal radii of the parabola y² = 4ax. For P, which of the following are true?

(a)   Vertex is (a/2,0)

(b)   Latus rectum is 2a

(c)   Directrix is x = a/2

(d)  Directrix x = 0

Answer 1

Correct option  : (A), (B), (D)

Explanation 

 Let Q (at², 2at) be a point on the parabola and S = (a, 0). M(x, y) is the midpoint of SQ. This implies

x = at² + a/2  and y = at

Now

Therefore, the vertex is (a/2,0) the latus rectum is 2a and the directrix equation is

x - a/2 = a/2 ⇒ x = 0