Question

Consider the parabola $y^2=4x$. Let $P$ and $Q$ be points on the parabola where $P(4,-4)$ and $Q(9,6)$. Let $R$ be a point on the arc of the parabola between $P$ and $Q$. Then the area of $△PQR$ is largest when

• A. $\angle PQR={90}^o$
• B. $R(4,4)$
• C. $R(\frac{1}{4},1)$
• D. $R(1,\frac{1}{4})$

Answer 1

The correct option is C $R(\frac{1}{4},1)$

$PQ\to 2x-y=12$
$perpendiculardistanceR{L}^2=\frac{(2t^2-2t-12{)}^2}{5}$
for maximum $t=\frac{2}{2\ast 2}=\frac{1}{2}$
$R=(\frac{1}{4},1)$