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The locus of a point, from where the tan...

The locus of a point, from where the tangents to the rect angular hyperbola `x^2 - y^2 = a^2` acontain an angle of `45^@` , is

A

`(x^2 +y^2 )^(2) +a^(2) (x^2-y^2) = 4a^2`

B

`2(x^2 +y^2 )^(2) +4a^(2) (x^2-y^2) = 4a^2`

C

`(x^2 +y^2 )^(2) +4a^(2) (x^2-y^2) = 4a^2`

D

`(x^2 +y^2 )^(2) +a^(2) (x^2-y^2) = a^2`

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The correct Answer is:
C
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