Tangents From a Moving Chord

★ 7/10conic sections AM-GM analytic geometry Vieta's Formulas

Problem

A line through the fixed point $P(1, 1)$ meets the parabola $x^2 = 4y$ at $A$ and $B$ . The tangent lines $\ell_1, \ell_2$ at $A$ and $B$ meet at $C$ .

1. Find the equation of the locus of $C$ . 2. Find the minimum area of $\triangle ABC$ .

Answer

Solution

Difficulty	7/10
Topics	conic sections, AM-GM, analytic geometry, Vieta's Formulas

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