The equation of a circle, which passes through the centre of the circle $x^2+y^2+8 x+10 y-7=0$ and is…

The equation of a circle, which passes through the centre of the circle $x^2+y^2+8 x+10 y-7=0$ and is concentric with the circle. $2 x^2+2 y^2-8 x-12 y-9=0$, is
  1. $x^2+y^2-4 x+6 y-87=0$
  2. $x^2+y^2+4 x+6 y-87=0$
  3. $x^2+y^2+4 x+6 y+87=0$
  4. $x^2+y^2-4 x-6 y-87=0$

Solution

The required circle is concentric with the circle $2 x^2+2 y^2-8 x-12 y-9=0$ i.e, centre is at $(2,3)$ and passes through the centre of the circle $x^2+y^2+8 x+10 y-7=0$ i.e., through $(-4,-5)$ Hence, the required equation is $\begin{aligned} & (x-2)^2+(y-3)^2=(2+4)^2+(3+5)^2 \\ & \Rightarrow x^2+y^2-4 x-6 y-87=0 \end{aligned}$

Asked in: MHT CET 2022 (10 Aug Shift 1)

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