A Max X Under a Vector Ratio

★ 7/10Extrema Substitution conic sections

Problem

Let $A$ and $B$ be two points on the ellipse $\dfrac{x^2}4+y^2=m$ ( $m>1$ ), with $P(0,1)$ and $\overrightarrow{AP}=2\overrightarrow{PB}$ . Find the maximum value of the $x$ -coordinate of $B$ .

Answer

Solution

Difficulty	7/10
Topics	Extrema, Substitution, conic sections

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