Consider the parabola y 2 = 8 x . Let Δ 1 be the area of the triangle formed by the end points of its latusrectum and the point P ( 2 1 , 2 ) on the parabola and Δ 2 be the area of the triangle

Question

Consider the parabola y 2 = 8 x . Let Δ 1 ​ be the area of the triangle formed by the end points of its latusrectum and the point P ( 2 1 ​ , 2 ) on the parabola and Δ 2 ​ be the area of the triangle formed by drawing tangents at P and at the end points of the latusrectum. Then, Δ 2 ​ Δ 1 ​ ​ is

TestHub · Accepted Answer

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

Mathematics - Parabola Question with Solution | TestHub

Doubts & Discussion