# The equation of a circle passing through the origin and cutting of intercepts each equal to +5 of the axis is  Option 1) $x^{2}+y^{2}+5x-5y=0$ Option 2) $x^{2}+y^{2}-5x+5y=0$ Option 3) $x^{2}+y^{2}-5x-5y=0$ Option 4) $x^{2}+y^{2}+5x+5y=0$

General form of a circle -

$x^{2}+y^{2}+2gx+2fy+c= 0$

- wherein

centre = $\left ( -g,-f \right )$

radius = $\sqrt{g^{2}+f^{2}-c}$

$x^{2}+y^{2}+2gx+2fy =0$

as it passes trough origin

Also

$25+10g =0\Rightarrow g=\frac{-5}{2}$

&   $25+10b =0 \Rightarrow f=\frac{-5}{2}$

so, $x^{2}+y^{2}-5x-5y =0$

Option 1)

$x^{2}+y^{2}+5x-5y=0$

Incorrect

Option 2)

$x^{2}+y^{2}-5x+5y=0$

Incorrect

Option 3)

$x^{2}+y^{2}-5x-5y=0$

Correct

Option 4)

$x^{2}+y^{2}+5x+5y=0$

Incorrect

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