Hello, shenton!

A point moves in such a way that it is always the same distance

from the point F(-3,-7) as it is from the line y = -1.

Determine the equation of the locus in standard form.

It might help you make a sketch . . .

Let P(x,y) be any point satisfying the restriction.

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The distance from F(-3,-7) to P(x,y) is: .FP .= .√(x + 3)² + (y + 7)²

The distance from P(x,y) to the line y = -1 is: .y + 1

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So we have: .√(x + 3)² + (y + 7)² .= .y + 1

Square: .x² + 6x + 9 + y² + 14y + 49 .= .y² + 2y + 1

. . x² + 6x + 9 .= .-12y - 48

. . (x + 3)² .= .-12(y + 4)

This is a down-opening parabola with vertex (-3, -4).