If the circles and touch each other

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

If the circles

x^2 + y^2 + (3 + \sin\theta)x + 2\cos\phi y = 0

and

x^2 + y^2 + (2\cos\phi)x + 2\lambda y = 0

touch each other, then the maximum value of

\lambda