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

Question

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 (A) 36 sq.units (B) 72 sq.units (C) 144 sq.units (D) 96 sq.units

Tardigrade Admin · Accepted Answer

(y - 2)2=-12x The quadrilateral is a square with diagonal length =12 <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-eqxurnya4nsn70pr.jpg" /> ∴ Area =(1/2)× 12× 12=72 sq. units

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

36 sq.units

72 sq.units

144 sq.units

96 sq.units

$(y - 2)^{2} = - 12 x$
The quadrilateral is a square with diagonal length
$= 12$

$∴$ Area $= \frac{1}{2} \times 12 \times 12 = 72$ sq. units

Q. 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