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From an external point P , a pair of tan...

From an external point `P ,` a pair of tangents is drawn to the parabola `y^2=4xdot` If `theta_1 and theta_2` are the inclinations of these tangents with the x-axis such that `theta_1+theta_2=pi/4` , then find the locus of `Pdot`

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The correct Answer is:
y=x-1
The equation of tangent to the parabola having slope m is `y=mx+(1)/(m)`
It passes through (h,k). Therefore,
`m^(2)h-mk+1=0`
`or" "m_(1)+m_(2)=(k.)/(h')m_(1)m_(2)=(1)/(h)`
Given `theta_(1)+theta_(2)=(pi)/(4)`
`or" "tan(theta_(1)+theta_(2))=1`
`or" "(m_(1)+m_(2))/(1-m_(1)m_(2))=1`
`or" "(k)/(h)=1-(1)/(h)`
`or" "y=x-1`
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