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A tangent line L is drawn at the point (2, -4) on the parabola y² = 8x. If the line L is also tangent to the circle $x^{2} + y^{2} =$ a, then ‘a’ is equal to ________.

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Vishal Baghel | Contributor-Level 10

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The tangent to the parabola

$y^{2} = 8 x a t (2, - 4) i s - 4 y = 4 (x + 2)$

x + y + 2 = 0

$O A = \sqrt[]{a}$

$\Rightarrow | \frac{0 + 0 + 2}{\sqrt[]{2}} | = \sqrt[]{a}$

$\sqrt[]{2} = \sqrt[]{a}$

a = 2

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...more

Slope of axis = $\frac{1}{2}$

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⇒ 2y – x – 4 = 0

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A tangent line L is drawn at the point (2, -4) on the parabola y² = 8x. If the line L is also tangent to the circle $x^{2} + y^{2} =$ a, then ‘a’ is equal to ________.

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A tangent line L is drawn at the point (2, -4) on the parabola y2 = 8x. If the line L is also tangent to the circle x 2 + y 2 = a, then ‘a’ is equal to ________.

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A tangent line L is drawn at the point (2, -4) on the parabola y² = 8x. If the line L is also tangent to the circle $x^{2} + y^{2} =$ a, then ‘a’ is equal to ________.