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

Answer 2

Here, $S \equiv y^{2} - 4x = 0$; $S(1,3) = 3^{2} - 4.1 > 0$⇒$P(1,3)$ is an

exterior point.

$S(1,1)$ = $1^{2} - 4.1 < 0$⇒ $Q(1,1)$ is an interior point.