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Problem 14

For what values of \(l\) and \(m\), circle \(5\left(x^{2}+y^{2}\right)+b y-m=0\) belongs to the co-axial system determined by the circles $x^{2}+y^{2}+2 x+4 y-6=0\( and \)2\left(x^{2}+y^{2}\right)-x=0 ?$

Expert verified

The values of \(l\) and \(m\) that make the given circle belong to the coaxial system determined by the two provided circles are \(2\) and approximately \(1.06\) respectively.

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