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If the normals to the parabola y^2=4a x ...

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 `Q Q '` is

A

10a

B

4a

C

20a

D

12a

Text Solution

Verified by Experts

The correct Answer is:
D
(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.
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CENGAGE PUBLICATION-PARABOLA-EXERCISE (SINGLE CORRECT ANSWER TYPE )
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