"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 x2 + y2 = a, then 'a' is equal to ___________."

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Accepted Answer

"tangent of y² = 8x is y = mx + ${2 \over m}$

P(2, $-$4) $\Rightarrow$ $-$4 = 2m + ${2 \over m}$

$\Rightarrow$ m + ${1 \over m}$ = $-$2 $\Rightarrow$ m = $-$1

$\therefore$ tangent is y = $-$x $-$2

$\Rightarrow$ x + y + 2 = 0 ...... (1)

(1) is also tangent to x² + y² = a

So, ${2 \over {\sqrt 2 }} = \sqrt a \Rightarrow \sqrt a = \sqrt 2$

$\Rightarrow$ a = 2"

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 x² + y² = 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 x2 + y2 = 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 x² + y² = a, then 'a' is equal to ___________.