Question

The equation of a parabola is $y^2=4x$. $P(1,3)$ and $Q(1,1)$ are two points in the $xy$-plane. Then, for the parabola

• A. $P$ and $Q$ are exterior points
• B. $P$ is an interior point while $Q$ is an exterior point
• C. $P$ and $Q$ are interior points
• D. $P$ is an exterior point while $Q$ is an interior point

Answer 1

Answer: (D)

$P$ is an exterior point while $Q$ is an interior point

Let $S=y^2-4x=0$
At point $(1,3),S_1=3^2-4>0$
$\Rightarrow P(1,3)$ is an exterior point.
At point $(1,1),S_2=1-4<0$
$\Rightarrow Q(1,1)$ is an interior point.