Question

Set of values of $a$ for which point $P(2,4)$ lies inside the parabola $y^2=4ax$ is

• A. $a\in (-\infty ,-2)$
• B. $a\in (-2,\infty )$
• C. $a\in (-\infty ,2)$
• D. $a\in (2,\infty )$

Answer 1

The correct option is D $a\in (2,\infty )$

$y^2=4ax\Rightarrow S=y^2-4ax$
$P(2,4)$ lies inside parabola, so
$S_1=4^2-4\times a\times 2<0$
$\Rightarrow 2-a<0$
$\Rightarrow a>2$
Hence, $a\in (2,\infty )$