If the points A(2,3) and B(3,2) form a triang | vedclass

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(B) Let the centroid of triangle $ABP$ be $G(x, y)$.The coordinates of the vertices are $A(2, 3)$,$B(3, 2)$,and $P(t, t^2)$.The centroid $G(x, y)$ is

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$3x^2 - 10x - y + 10 = 0$

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(B) Let the centroid of triangle $ABP$ be $G(x, y)$.The coordinates of the vertices are $A(2, 3)$,$B(3, 2)$,and $P(t, t^2)$.The centroid $G(x, y)$ is given by the formula:$x = \frac{2 + 3 + t}{3} \implies 3x = 5 + t \implies t = 3x - 5$$y = \frac{3 + 2 + t^2}{3} \implies 3y = 5 + t^2$Substitute $t = 3x - 5$ into the equation for $y$:$3y = 5 + (3x - 5)^2$$3y = 5 + 9x^2 - 30x + 25$$3y = 9x^2 - 30x + 30$Dividing by $3$:$y = 3x^2 - 10x + 10$Rearranging the terms:$3x^2 - 10x - y + 10 = 0$Thus,the locus of the centroid is $3x^2 - 10x - y + 10 = 0$.

If the points $A(2,3)$ and $B(3,2)$ form a triangle with a variable point $P(t, t^2)$,where $t$ is a parameter,then the equation of the locus of the centroid of triangle $ABP$ is:

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