AP EAMCET · Maths · Circle
The equation of the circle whose diameter is the common chord of the circles \(x^2+y^2-6 x-7=0\) and \(x^2+y^2-10 x+16=0\), is
- A \(8 x^2+8 y^2-92 x+197=0\)
- B \(x^2+y^2-23 x+197=0\)
- C \(x^2+y^2-\frac{23}{2} x+\frac{197}{4}=0\)
- D \(4 x^2+4 y^2-46 x+197=0\)
Answer & Solution
Correct Answer
(A) \(8 x^2+8 y^2-92 x+197=0\)
Step-by-step Solution
Detailed explanation
\(S_1 \equiv x^2+y^2-6 x-7=0\) \(\begin{aligned} & \mathrm{S}_2 \equiv x^2+y^2-10 x+16=0 \\ & \mathrm{~S}_1-\mathrm{S}_2=4 x-23=0 \Rightarrow x=\frac{23}{4} \Rightarrow y= \pm \frac{\sqrt{135}}{4}= \pm \frac{3 \sqrt{15}}{4} \end{aligned}\) Co-ordinates of diameter are…
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