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(D) The required circle is concentric with $2x^2+2y^2-8x-12y-9=0$. Dividing by $2$,we get $x^2+y^2-4x-6y-\frac{9}{2}=0$. Thus,the centre of the requir

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$x^2+y^2-4x-6y-87=0$

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(D) The required circle is concentric with $2x^2+2y^2-8x-12y-9=0$. Dividing by $2$,we get $x^2+y^2-4x-6y-\frac{9}{2}=0$. Thus,the centre of the required circle is $(2, 3)$. The circle passes through the centre of $x^2+y^2+8x+10y-7=0$. Comparing with $x^2+y^2+2gx+2fy+c=0$,the centre is $(-4, -5)$. The radius $r$ is the distance between $(2, 3)$ and $(-4, -5)$: $r = \sqrt{(-4-2)^2 + (-5-3)^2} = \sqrt{(-6)^2 + (-8)^2} = \sqrt{36+64} = 10$. The equation of the circle is $(x-2)^2 + (y-3)^2 = 10^2$. $x^2-4x+4 + y^2-6y+9 = 100$. $x^2+y^2-4x-6y-87=0$.

The equation of the circle which passes through the centre of the circle $x^2+y^2+8x+10y-7=0$ and is concentric with the circle $2x^2+2y^2-8x-12y-9=0$ is

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