Question

Let $A(4,-4)$ and $B(9,6)$ be points on the parabola, $y^2 + 4x$. Let $C$ be chosen on the arc $AOB$ of the parabola, where $O$ is the origin, such that the area of $\Delta ACB$ is maximum. Then, the area (in s units) of $\Delta ACB$, is :

• A. $31 \frac{3}{4}$
• B. 32
• C. $30 \frac{1}{2}$
• D. $31 \frac{1}{4}$

Answer 1

The Correct Option is D

Area $= 5\left|t^{2} -t -6\right| = 5 \left| \left(t - \frac{1}{2}\right)^{2} - \frac{25}{4}\right| $
is maximum if $t = \frac{1}{2}$