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Position of a Point W.R.T Parabola

The value of ...

Question

$The value of a for which the point (a, 2 a) lies in the interior region of the parabola y^{2} = 16 x is$
.

0 < a < 4

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0 < a < 8

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- 4 < a < 0

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- 8 < a < 0

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Solution

The correct option is A $0 < a < 4$
If $(a, 2 a)$ lies inside the parabola $y^{2} = 16 x$ , then
$(2 a)^{2} - 16 a < 0 \Rightarrow a (a - 4) < 0 \Rightarrow 0 < a < 4$

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