If the centre of the circle $2 x^{2} + p x y + q y^{2} + 2 g x + 2 f y + 3$ = 0 is (1,-3), then the radius of the circle is

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Solution

The correct option is D

$2 x^{2} + p x y + q y^{+} 2 g x + 2 f y + 3$ = 0

$\Rightarrow 2 x^{2} + 2 y^{2} + 2 g x + 2 f y + 3$

$\Rightarrow x^{2} + y^{2} + g x + f y + (\frac{3}{2})$ = 0

C = $(- \frac{g}{2}, - \frac{f}{2})$ = (1,-3) , g = -2,f = 6

C=(1,-3)

r= $\sqrt{4 + 36 - \frac{3}{2}}$ = $\sqrt{\frac{77}{2}}$

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