# If one of the diameters of the circle, given by the equation, x2 + y2 − 4x + 6y − 12=0, is a chord of a circle S, whose centre is at (−3, 2), then the radius of S is : Option 1) Option 2) Option 3) 5 Option 4) 10

As we learnt in

General form of a circle -

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

- wherein

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

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

Distance between centres=$C_{1}\left ( 2,-3 \right )$ and $C_{2}\left ( -3,1 \right )$

$C_{1} C_{2}=d=\sqrt{\left ( 2+3^\right )^2+\left ( -3-2 \right )^2}=\sqrt{50}$$=5\sqrt{2}$

Now $R^{2}=r^{2}+d^{2}$

$= 25+50=75$

$R=5\sqrt{3}$

Option 1)

Incorrect option

Option 2)

Correct option

Option 3)

5

Incorrect option

Option 4)

10

Incorrect option

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