What does the equation sqrt{(x - 2)^2 + (y + | vedclass

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(C) The given equation is of the form $PF_1 + PF_2 = 2a$,where $P = (x, y)$,$F_1 = (2, -1)$,and $F_2 = (-2, -4)$.First,calculate the distance between

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(C) The given equation is of the form $PF_1 + PF_2 = 2a$,where $P = (x, y)$,$F_1 = (2, -1)$,and $F_2 = (-2, -4)$.First,calculate the distance between the two fixed points $F_1$ and $F_2$:$d = \sqrt{(2 - (-2))^2 + (-1 - (-4))^2} = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5$.Here,the sum of the distances from point $P$ to two fixed points $F_1$ and $F_2$ is equal to the distance between the two fixed points $(PF_1 + PF_2 = F_1F_2 = 5)$.When the sum of distances from a point to two fixed points equals the distance between the fixed points,the locus of the point $P$ is the line segment joining the two fixed points $F_1$ and $F_2$.Therefore,the equation represents a line segment.

What does the equation $\sqrt{(x - 2)^2 + (y + 1)^2} + \sqrt{(x + 2)^2 + (y + 4)^2} = 5$ represent?

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