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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 `P` meets the curve again at `Q` and if `P Q` and the normal at `Q` make angle `alpha` and`beta` , respectively, with the x-axis, then `t a nalpha(tanalpha+tanbeta)` has the value equal to 0 (b) `-2` (c) `-1/2` (d) `-1`

A

0

B

-2

C

`-1//2`

D

-1

Text Solution

Verified by Experts

The correct Answer is:
B
(2) `tanalpha=-t_(1)andtantanbeta=-t_(2)`
Also, `t_(2)=-t_(1)-(2)/(t_(1))`
`t_(1)t_(2)+t_(1)^(2)=-2`
`tanalphatanbeta+tan^(2)alpha=-2`
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