Question

If $\left(\right. 9 a , 6 a \left.\right)$ is a point bounded in the region formed by parabola $y^{2} = 16 x$ and $x = 9 ,$ then

• A. $a\in \left(\right.0,1\left.\right)$
• B. $a < \frac{1}{4}$
• C. $a < 1$
• D. $0 < a < 4$

Answer 1

Answer: (A)

Since, the point $\left(\right. 9 a , 6 a \left.\right)$ is bounded in the region formed by the parabola $y^{2} = 16$ and $x = 9 ,$ then

$y^{2}-16x < 0,x-9 < 0$
$\Rightarrow 36a^{2}-16\left(9 a\right) < 0,9a-9 < 0$
$36a\left(\right. a - 4 \left.\right) < 0, \, \, 9a-9 < 0$
$0 < a < 4,a < 1\Rightarrow 0 < a < 1$