AP EAMCET · Maths · Circle
Find the area of the circle
\[
(x+1)(x+2)+(y-1)(y+3)=0
\]
- A \(\frac{17 \pi}{4}\)
- B \(\frac{17 \pi}{2}\)
- C \(\frac{2 \pi}{17}\)
- D \(\frac{\pi}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{17 \pi}{4}\)
Step-by-step Solution
Detailed explanation
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.
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