A Parabola Parameter Duo

★ 7/10Parametrization conic sections AM-GM analytic geometry

Problem

Let $O$ be the origin and $F$ the focus of the parabola $C \colon y^2 = x$ . Points $A, B$ lie on $C$ with $OA \perp AB$ .

1. When $\angle AOF = 45^\circ$ , find $|AB|$ . 2. Find the minimum value of $3|FA| + |FB|$ .

Answer

Solution

Difficulty	7/10
Topics	Parametrization, conic sections, AM-GM, analytic geometry

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