Q114 / 160 · AP EAMCET 2020 (22 Sep Shift 2) · Mathematics
Find the area of the circle
$$
(x+1)(x+2)+(y-1)(y+3)=0
$$
- Correct answerA$\frac{17 \pi}{4}$
- B$\frac{17 \pi}{2}$
- C$\frac{2 \pi}{17}$
- D$\frac{\pi}{3}$
Solution
Given circle is,
$$
\begin{aligned}
&(x+1)(x+2)+(y-1)(y+3)=0 \\
& x^2+y^2+3 x+2 y-1=0 \\
& 2 g=3 \\
& g=\frac{3}{2} \\
& 2 f=2 \\
& f=1 \\
& c=-1 \\
& r=\sqrt{g^2+f^2-c}=\sqrt{\frac{9}{4}+1+1} \\
& r=\sqrt{\frac{17}{4}}
\end{aligned}
$$
Hence, option (1) is correct.
Hence, the correct answer is option: 'A'.