The locus of the moving point P,such that 2PA | vedclass

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(D) Let the coordinates of point $P$ be $(h, k)$.Given the condition $2PA = 3PB$,we square both sides to get $4PA^2 = 9PB^2$.Substituting the coordina

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$5x^2 + 5y^2 - 72x + 54y + 225 = 0$

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(D) Let the coordinates of point $P$ be $(h, k)$.Given the condition $2PA = 3PB$,we square both sides to get $4PA^2 = 9PB^2$.Substituting the coordinates $A(0, 0)$ and $B(4, -3)$,we have:$4(h^2 + k^2) = 9((h - 4)^2 + (k + 3)^2)$$4h^2 + 4k^2 = 9(h^2 - 8h + 16 + k^2 + 6k + 9)$$4h^2 + 4k^2 = 9h^2 - 72h + 144 + 9k^2 + 54k + 81$Rearranging the terms to one side:$5h^2 + 5k^2 - 72h + 54k + 225 = 0$Replacing $(h, k)$ with $(x, y)$,the locus of point $P$ is:$5x^2 + 5y^2 - 72x + 54y + 225 = 0$.

The locus of the moving point $P$,such that $2PA = 3PB$ where $A$ is $(0,0)$ and $B$ is $(4,-3)$,is

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