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  • Find the equation of a circle concentric with the circle x^2 + y^2 – 6x + 12y + 15 = 0 and has double of its area.

Find the equation of a circle concentric with the circle x2 + y2 – 6x + 12y + 15 = 0 and has double of its area.

Answers (1)

Given equation of the circle is : 

x2+y2-6x+12y+15=0

(x-3)2+(y+6)2=(30)  

 Hence, centre is (3, -6) and radius is \sqrt{30 }

 Since, the required circle is concentric with above circle, centre of the required circle is (3, -6). 

Let its radius be r

Area of circle=\Pi r^{2}=2\pi\left (\sqrt{30 } \right )^{2}

r2=60

r = \sqrt{60}

Equation of required circle (x-3)2+(y+6)2=60

x2+y2-6x+12y-15=0

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