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`

Options

A. 0
B. -2
C. `-1//2`
D. -1

Answer

B

Explanation

(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`