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  • A tangent line is drawn at the point <img alt="\mathrm{(2,-4)}" src="https://entrancecorner.oncodecog

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

Option: 1

2


Option: 2

4


Option: 3

6


Option: 4

0


Answers (1)

best_answer

Equation of tangent at \mathrm{(2,-4)\: to \: y^2=8 x} is

\mathrm{ -4 y=4(x+2) }

\mathrm{ \Rightarrow y=-x-2 }         .......(i)
\mathrm{ \because \quad (i) \text{is also a tangent to the circle} x^2+y^2=a }

\mathrm{ \therefore \quad \sqrt{a}=\left|\frac{-2}{\sqrt{1+(-1)^2}}\right| }

\mathrm{ \Rightarrow \quad a=\left|\frac{4}{2}\right|=2 }
 

Posted by

Suraj Bhandari

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