# 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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