Discussion Forum

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

Answer:

Explanation:

As, we know area of triangle formed by three points on the parabola is twice the area of the triangle formed by corresponding tangents i.e, area of $\triangle PQR$=2 area   of $\triangle T_{1}T_{2}T_{3}$

 $\triangle _{1}=2 \triangle _{2}$ or $\frac{ \triangle_{1}}{\triangle_{2}}=2$