AP EAMCET · Maths · Circle
If the line \(3 x-2 y+6=0\) meets \(X\)-axis and \(Y\)-axis, respectively at \(A\) and \(B\), then the equation of the circle with radius \(A B\) and centre at \(A\) is
- A \(x^2+y^2+4 x+9=0\)
- B \(x^2+y^2+4 x-9=0\)
- C \(x^2+y^2+4 x+4=0\)
- D \(x^2+y^2+4 x-4=0\)
Answer & Solution
Correct Answer
(B) \(x^2+y^2+4 x-9=0\)
Step-by-step Solution
Detailed explanation
Since, the line \(3 x-2 y+6=0\) meets the coordinates axes, therefore \(\therefore\) Points are \(A(-2,0)\) and \(B(0,3)\). \[ \because \text { Radius }=A B=\sqrt{2^2+3^2}=\sqrt{13} \] \(\therefore\) The equation of circle, whose centre \((-2,0)\) and radius \(\sqrt{13}\), is…
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