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  4. The line 4 x-7 y+10=0 intersects the parabola, y2=4 x at the points A and B. The sum of the co-ordinates of the point of intersection of the tangents drawn at the points A and B is

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Q. The line $4 x-7 y+10=0$ intersects the parabola, $y^2=4 x$ at the points $A$ and $B$. The sum of the co-ordinates of the point of intersection of the tangents drawn at the points $A$ and $B$ is

Conic Sections

Solution:

image
C.O.C. of $P \left( x _1, y _1\right)$
w.r.t. $y ^2=4 ax$ is
$yy _1=2\left( x + x _1\right)$ ....(1)
compare with
$4 x-7 y+10=0 $ .....(2)
$\text { to get }\left(x_1, y_1\right)=\left(\frac{5}{2}, \frac{7}{2}\right)$