If the angle between tangents drawn to $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ from $(0, 0)$ is $\frac{π}{2}$ , then

g^{2} + f^{2} = 3 c

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g^{2} + f^{2} = 2 c

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g^{2} + f^{2} = 5 c

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g^{2} + f^{2} = 4 c

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Solution

The correct option is B $g^{2} + f^{2} = 2 c$
Clearly $(0, 0)$ lies on director circle of the given circle.
Now, equation of director circle is
$(x + g)^{2} + (y + f)^{2} = 2 (g^{2} + f^{2} - c)$
If (0, 0) lies on it, then
$g^{2} + f^{2} = 2 (f^{2} + f^{2} - c)$
$\Rightarrow g^{2} + f^{2} = 2 c$

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Similar questions

x^{2} + y^{2} + 2 g x + 2 f y + c = 0

(c > 0)

\frac{π}{2},

An equilateral triangle inscribed in the circle $x^{2} + y^{2} + 2 g x + 2 f y + c$ = 0 then its side is

x^{2} + y^{2} + 2 g x + 2 f y + c = 0

g^{2} + f^{2} = c,

x^{2} + y^{2} + 2 g x + 2 f y + c = 0

g^{2} < c < f^{2}

x^{2} + y^{2} + 2 g x + 2 f y + c = 0

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