AP EAMCET · Maths · Circle
If the circle \(x^2+y^2+2 x+3 y+1=0\) cuts another circle \(x^2+y^2+4 x+3 y+2=0\) in \(A\) and \(B\), then the equation of the circle with \(A B\) as a diameter is
- A \(x^2+y^2+x+3 y+3=0\)
- B \(2 x^2+2 y^2+2 x+6 y+1=0\)
- C \(x^2+y^2+x+6 y+1=0\)
- D \(2 x^2+2 y^2+x+3 y+1=0\)
Answer & Solution
Correct Answer
(B) \(2 x^2+2 y^2+2 x+6 y+1=0\)
Step-by-step Solution
Detailed explanation
The equation of the circles are \(S_1 \equiv x^2+y^2+2 x+3 y+1=0\) and \(S_2 \equiv x^2+y^2+4 x+3 y+2=0\) Since, the circles cuts each other at \(A\) and \(B\) then equation of \(A B\) is \(S_1-S_2=0\) \(\Rightarrow \quad\left(x^2+y^2+2 x+3 y+1\right)\)…
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