Question

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

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

Answer 1

Answer: (D)

$31\frac{1}{4}$

Area $=5|t^2-t-6|$

$=5|(t-\frac{1}{2}{)}^2-\frac{25}{4}|$

Area is maximum when $t=\frac{1}{2}$

therefore Area $=31\frac{1}{4}$