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Problem 6

The circle \(x^{2}+y^{2}=4\) cuts the circle \(x^{2}+y^{2}+2 x+3 y-5=0\) in \(A\) and \(B\), the centre of the circle \(A B\) as diameter is : (a) \((0,0)\) (b) \(\left(\frac{2}{13}, \frac{3}{13}\right)\) (c) \(\left(\frac{4}{13}, \frac{6}{13}\right)\) (d) \((2,-1)\)

Expert verified

The center of the circle AB is \(\left(\frac{2}{13}, \frac{3}{13}\right)\). This corresponds with answer option (b).

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Chapter 1

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