Home Maths Conic Sections General The locus of the mid point of the focal radi…
Maths Conic Sections General More Than One Correct MCQ
Published on: August 14, 2026

The locus of the mid point of the focal radii of a variable point moving on the parabola, y 2 = 4ax is a parabola whose

A
Latus rectum is half the latus rectum of the original parabola
B
Vertex is (a/2, 0)
C
Directrix is y-axis
D
Focus has the co-ordinates (a,0)

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The correct answer is:
CHECK THE SOLUTION.

(a,b,c,d)

h = , k = ⇒ α = 2h – a, β = 2k

α , β satisfies the parabola

∴ β 2 = 4a α ⇒ 4k 2 = 4a(2h – a) ⇒ y 2 = a(2x – a) ⇒ y 2 = 2a

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