Q93 / 160 · TS EAMCET 2019 (04 May Shift 1) · Mathematics
The equation of a circle concentric with the circle $x^2+y^2-6 x+12 y+15=0$ and having area that is twice the area of the given circle is
- Correct answerA$x^2+y^2-6 x+12 y-15=0$
- B$x^2+y^2-6 x+12 y-30=0$
- C$x^2+y^2-6 x+12 y-60=0$
- D$x^2+y^2-6 x+12 y+15=0$
Solution
Given,
$$
x^2+y^2-6 x+12 y+15=0
$$
Centre (3,-6)
$$
r=\sqrt{9+36-15}=\sqrt{30}
$$
Area $\quad=\pi(\sqrt{30})^2=30 \pi$
Required equation of circle has twice the area of circle
$$
\therefore \quad \begin{aligned}
A^{\prime} & =60 \pi \\
\pi R^2 & =60 \pi, R^2=60
\end{aligned}
$$
$\therefore$ Equation of circle concentric with given circle is
$$
\begin{aligned}
(x-3)^2+(y+6)^2 & =60 \\
x^2+y^2-6 x+12 y-15 & =0
\end{aligned}
$$
Hence, the correct answer is option: 'A'.