If (. 9 a , 6 a .) is a point bounded in the region formed by parabola y2 = 16 x and x = 9 , then

Question

If (. 9 a , 6 a .) is a point bounded in the region formed by parabola y2 = 16 x and x = 9 , then (A) a∈ (.0,1.) (B) a < (1/4) (C) a < 1 (D) 0 < a < 4

Tardigrade Admin · Accepted Answer

Since, the point (. 9 a , 6 a .) is bounded in the region formed by the parabola y2 = 16 and x = 9 , then <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-9o6fcjki9vcb.png" /> y2-16x < 0,x-9 < 0 ⇒ 36a2-16(9 a) < 0,9a-9 < 0 36a(. a - 4 .) < 0, 9a-9 < 0 0 < a < 4,a < 1⇒ 0 < a < 1

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

$a \in (0, 1)$

$a < \frac{1}{4}$

$a < 1$

$0 < a < 4$

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

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

Q. If (9a,6a) is a point bounded in the region formed by parabola y2=16x and x=9, then

a∈(0,1)

a<41​

a<1

0<a<4