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The lines y = 2x + sqrt 76 and 2y + x=8 ...

The lines `y = 2x + sqrt 76 and 2y + x=8 `touch the ellipse `(x ^(2))/(16 )+(y ^(2))/(12)=1.`If the point of intersection of these two lines lie on a circle, whose centre coincides with the centre of that ellipse, then the equation of that circle is

A

`x ^(2) + y^(2) =16`

B

`x ^(2) + y^(2)=12`

C

`x ^(2) + y^(2)=28`

D

`x ^(2) + y^(2) =(4+sqrt8)^(2)`

Text Solution

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The correct Answer is:
C
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