Is That Lambda Of Any Use?

Geometry Level 4

Suppose \(P\) is a point on the line \(x-y=0\) . \(PA\) and \(PB\) are the lengths of tangents drawn from \(P\) to the circles whose equations are \(x^2+y^2+2\lambda x + 5=0\) and \(x^2+y^2+2\lambda y + 5=0\) respectively, such that \(PA=3\) . Evaluate \(PB\) to correct two decimal places.

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