# Fun with conics

Geometry Level 5

Consider the parabola $$y^{2} = 4x$$ and the ellipse $$\dfrac{x^{2}}{9} + \dfrac{y^{2}}{4} = 1$$.

The tangent line of positive slope that is common to these two curves has a $$y$$-intercept of the form $$\sqrt{a + \sqrt{b}}$$, where $$a$$ and $$b$$ are positive integers and $$b$$ is square-free. Find $$a + b$$.

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