Question

Consider the parabola $y^2=8x$. Let ${\Delta }_1$ be the area of the triangle formed by the endpoints of its latus rectum and the points $P(\frac{1}{2},2)$ on the parabola and ${\Delta }_2$ be the area of the triangle formed by drawing tangents at P and at the endpoints of the latus rectum. Then,$\frac{{\Delta }_1}{{\Delta }_2}$ is ___

Answer 1

Area of a triangle formed by three points on parabola is twice the area of the triangle formed by corresponding tangents i.e. area of $\Delta PQR=2$ (area of $\Delta T_1{T}_2{T}_3$).
$\therefore {\Delta }_1=2{\Delta }_{2}or\frac{{\Delta }_1}{{\Delta }_2}=2$