The parabola with vertex (7,-2) and directrix y = -3

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Question from Deann, a student:

Find an equation of the parabola with vertex (7,-2) and directrix y =(-3)

Hi Deann,

Since the directrix is y = -3 and the vertex is (7,-2) you can draw a rough sketch.

parabola

The distance from the vertex to the directrix is 1 unit. Since every point on a parabola is the same distance from the directrix as it is from the focus the focus must be at (7,-1). Can you write the equation of the parabola with directrix y = -3 and focus (7,-1)?

Penny

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