From an external point P, a pair of tangents is drawn to the parabola `y^(2)=4x`. If `theta_(1)andtheta_(2)` are the inclinations of these tangent with the x-axis such that `theta_(1)+theta_(2)=pi//4`, then find the locus of P.

Options

A. `x - y +1 = 0`
B. `x +y - 1 = 0`
C. `x - y - 1 = 0`
D. `x +y + 1 = 0`

Answer

C

Explanation

Equation of tangent having slope m is `y = mx +(1)/(m)`, which passes through the point (h,k).
`:. m^(2) h - mk +1 =0`
`:. m_(1) + m_(2) = (k)/(h), m_(1)m_(2) = (1)/(h)`
Given `theta_(1) + theta_(2) = (pi)/(4)`
`rArr (m_(1)+m_(2))/(1-m_(2)m_(2)) =1`
`rArr (k)/(h) =1 -(1)/(h)`
`rArr y = x-1`