Let $A(2,-1)$ and $B(5,3)$ be two fixed points and let $M$ be their midpoint. Determine the equation of the locus of a point $P(x,y)$ that satisfies $PA^{2}+PB^{2}=4\,PM^{2}$. Then compute the area enclosed by this locus, expressing your answer in terms of $\pi$.

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Accepted Answer

(x-3.5)^2 + (y-1)^2 = 6.25 ; area = 6.25π

Neco Model Questions Vol1 2023 Mathematics Question 39

Let \(A(2,-1)\) and \(B(5,3)\) be two fixed points and let \(M\) be their midpoint. Determine the equation of the locus of a point \(P(x,y)\) that satisfies \(PA^{2}+PB^{2}=4\,PM^{2}\). Then compute the area enclosed by this locus, expressing your answer in terms of \(\pi\).

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