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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Parabola

NTA Abhyas 2020 · Mathematics · Parabola

If ( 9a, 6a ) is a point bounded in the region formed by parabola...

If (9a,6a)( 9a, 6a ) is a point bounded in the region formed by parabola y2=16xy^{2} = 16x and x=9,x = 9, thenIf ( 9a, 6a ) is a point bounded in the region formed by parabola y^ 2 = 16x and x = 9, then

Options

  1. Aa∈(0,1)a \in (0,1)
  2. Ba<14a < \dfrac{1}{4}
  3. Ca<1a < 1
  4. D0<a<40 < a < 4

Correct answer

A. a∈(0,1)a \in (0,1)

Step-by-step solution

Since, the point (9a,6a)( 9a, 6a ) is bounded in the region formed by the parabola y2=16y^{2} = 16 and x=9,x = 9, then

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

y2−16x<0,x−9<0y^{2} - 16x < 0, x - 9 < 0

⇒36a2−16(9a)<0,9a−9<0⇒ 36a^{2} - 16\left(9a\right) < 0, 9a - 9 < 0

36a(a−4)<0,9a−9<036a( a - 4 ) < 0, 9a - 9 < 0

0<a<4,a<1⇒0<a<10 < a < 4, a < 1 ⇒ 0 < a < 1
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