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  4. The area of the quadrilateral formed by the tangents and normals at the extremities of the latus rectum of the parabola y2-4y+4+12x=0 is

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Q. The area of the quadrilateral formed by the tangents and normals at the extremities of the latus rectum of the parabola $y^{2}-4y+4+12x=0$ is

NTA AbhyasNTA Abhyas 2022

Solution:

$\left(y - 2\right)^{2}=-12x$
The quadrilateral is a square with diagonal length
$=12$
Solution
$\therefore $ Area $=\frac{1}{2}\times 12\times 12=72$ sq. units