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)

    5\sqrt{2}

  • Option 2)

    5\sqrt{3}

  • Option 3)

    5

  • Option 4)

    10

 

Answers (1)

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}

 

 Radius of given circle =5

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)

5\sqrt{2}

Incorrect option

Option 2)

5\sqrt{3}

Correct option

Option 3)

5

Incorrect option

Option 4)

10

Incorrect option

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