NTA Abhyas JEE Main2020MathematicsParabolaPractice

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

Options

Aa ∈ ( 0,1 )
Ba < 1 4
Ca < 1
D0 < a < 4

Correct answer

A. a ∈ ( 0,1 )

Step-by-step solution

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 ⇒ 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 ⇒ 0 < a < 1

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