Question

The locus of the middle points of chords of the parabola $y^2=8x$ drawn through the vertex is a parabola whose

• A. focus is $(2,0)$
• B. latus rectrum = $8$
• C. focus is $(0,2)$
• D. latus rectrum = $4$

Answer 1

Answer: (D)

latus rectrum = $4$

coordinates of end points of chord of parabola $y^2=8x$ through vertex are $V(0,0)$ and $P(2t^2,4t)$
Therefore mid point of $VP$ is $(t^2,2t)$
$x=t^2,y=2t$ eliminating t we get locus $y^2=4x$ which has latus rectum $4.$