If the normals to the parabola `y^2=4a x` at the ends of the latus rectum meet the parabola at `Qa n dQ^(prime),` then `QQ '` is `10 a` (b) `4a` (c) `20 c` (d) `12 a`

Options

A. 10a
B. 4a
C. 20a
D. 12a

Answer

D

Explanation

(4) The ends of the latus rectum are P(a,2a)andP'(a,-2a).
Point P has parameter `t_(1)=1` and point P' has parameter `t_(2)=-1`.
Normal at point P meets the curve again at point Q whose parameter
`t_(1)'=-t_(1)-(2)/(t_(1))=-3`
Normal at point P meets the curve again at point Q whose parameter
`t_(2)'=-t_(2)-(2)/(t_(2))=-3`
Hence, point Q and Q' have coordinates (9a,-6a) and (9a,6a), respectively.
Hence, QQ'=12a.