question_answer

Let\[A\,(4,-\,\,4)\] and B(9, 6) be points on the parabola \[{{y}^{2}}=4x.\] be chosen on the arc AOB of the parabola, where O is the origin, such  the area of \[\Delta ACB\] is the area (in sq. units) of \[\Delta ACB\] is:

A) \[31\frac{3}{4}\]

B) 32

C) \[30\frac{1}{2}\]

D) \[30\frac{1}{4}\]

Correct Answer: D

Solution :

For maximum area, tangent at the point C must be parallel to chord BC.

\[\therefore \]      \[t=\frac{1}{2}.\]