If P is a variable point such that the sum of | vedclass

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(C) Let $P = (x, y)$. The given condition is $PA + PB = 4$. The distance between $A(2, 2)$ and $B(2, -2)$ is $d = \sqrt{(2-2)^2 + (2 - (-2))^2} = \sqr

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a segment of a vertical line

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(C) Let $P = (x, y)$. The given condition is $PA + PB = 4$. The distance between $A(2, 2)$ and $B(2, -2)$ is $d = \sqrt{(2-2)^2 + (2 - (-2))^2} = \sqrt{0^2 + 4^2} = 4$. Since the sum of the distances $PA + PB$ is equal to the distance between the fixed points $A$ and $B$ (i.e.,$PA + PB = AB = 4$),the point $P$ must lie on the line segment joining $A$ and $B$. The points $A(2, 2)$ and $B(2, -2)$ both have an $x$-coordinate of $2$,so the line segment connecting them is a vertical line segment. Therefore,the locus of $P$ is the segment of the vertical line $x = 2$ between $y = -2$ and $y = 2$.

If $P$ is a variable point such that the sum of the distances from $P$ to the points $A(2,2)$ and $B(2,-2)$ is $4$,then the locus of $P$ represents

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