Question

The point $(a,2a)$ is an interior point of the region bounded by the parabola $y^2=16x$ and the double ordinate through the focus. Then $a$ belongs to the open interval

• A. $a<4$
• B. $0<a<4$
• C. $0<a<2$
• D. $a>4$

Answer 1

The correct option is B $0<a<4$

Given parabola $y^2-16x=0$
Also given $(a,2a)$ is an interior point of the region bounded by the parabola
$\Rightarrow (2a{)}^2-16(a)<0$
$\Rightarrow 4a(a-4)<0$
$\Rightarrow a^2-4a<0$ ...(1)
$\Rightarrow a>0$ and $a<4$
$\Rightarrow 0<a<4$
Now the x-coordinate of the point must be between $0$ and $4$.
$\Rightarrow 0<a<4$.
Hence, option B is correct.