The equation of the circle, concentric with the circle $x^2+y^2-6 x-4 y-12=0$ and touching the X -axis is

The equation of the circle, concentric with the circle $x^2+y^2-6 x-4 y-12=0$ and touching the X -axis is
  1. $x^2+y^2-6 x-4 y+5=0$
  2. $x^2+y^2-6 x-4 y+17=0$
  3. $x^2+y^2-6 x-4 y+9=0$
  4. $x^2+y^2-6 x-4 y+4=0$

Solution

Centre of the circle $x^2+y^2-6 x-4 y-12=0 \text { is } \mathrm{C}(3,2)$
Since it touches X-axis, $\mathrm{r}=2$ Hence, the required equation of the circle is $\begin{aligned} & (x-3)^2+(y-2)^2=2^2 \\ & \Rightarrow x^2+y^2-6 x-4 y+9=0 \end{aligned}$

Asked in: MHT CET 2024 (09 May Shift 2)

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