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  4. The point of intersection of the perpendicular tangents to the parabola, y2=12 x, if slope of one of the tangents is 3 / 2 is

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Q. The point of intersection of the perpendicular tangents to the parabola, $y^{2}=12 x$, if slope of one of the tangents is $3 / 2$ is

KCETKCET 2022

Solution:

Point of intersection of the perpendicular tangents lies on the directrix, $x=-a=-3$.
Equation of the tangent having slope $3 / 2$ is $y=(3 / 2) x+\frac{3}{3 / 2}$.
By taking $x=-3$
we get, $y=-5 / 2$.