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  4. The chord of contact of the pair of tangents drawn from each point on the line 2 x+y=4 to the parabola y2=-4 x passes through a fixed point :

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Q. The chord of contact of the pair of tangents drawn from each point on the line $2 x+y=4$ to the parabola $y^2=-4 x$ passes through a fixed point :

Conic Sections

Solution:

equation of the chord of contact is $yy _1+2\left( x + x _1\right)=0$ where $2 x_1+y_1=4$ put $y_1=4-2 x_1$ in above and interpret the result