If the locus of the middle of point of contact of tangent drawn to the parabola `y^2=8x` and the foot of perpendicular drawn from its focus to the tangents is a conic, then the length of latus rectum of this conic is `9/4` (b) 9 (c) 18 (d) `9/2`

Options

A. `9//4`
B. 9
C. 18
D. `9//2`

Answer

B

Explanation

(2) Let the middle point of P and T be (h,k). Then,
`2h=at^(2)`
`and2k=3at`
`:.2h=a*(4k^(2))/(9a^(2))`
The locus of (h,k) is `2y^(2)=9ax`.
As a=2, we get `y^(2)=9x`.