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  4. Two tangent lines l1 and l2 are drawn from the point (2,0) to the parabola 2 y2=-x. If the lines l1 and l2 are also tangent to the circle (x-5)2+y2=r, then 17 r is equal to

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Q. Two tangent lines $l_1$ and $l_2$ are drawn from the point $(2,0)$ to the parabola $2 y^2=-x$. If the lines $l_1$ and $l_2$ are also tangent to the circle $(x-5)^2+y^2=r$, then $17 r$ is equal to

JEE MainJEE Main 2022Conic Sections

Solution:

$ y^2=-\frac{x}{2}$
$ y=m x-\frac{1}{8 m}$
this tangent pass through $(2,0)$
$m =\pm \frac{1}{4}$
i.e., one tangent is $x-4 y-2=0$
$17 r =9$