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Find the standard form of the equation of the parabola with a focus at (0, 2) and a directrix at y = - 2

1 Answer

1 vote

Answer:

y = `1/8x^2.

Explanation:

This is a parabola which opens upwards.

For any point P on the curve the distance of the point from the focus = the perpendicular distance of P from the directrix.

sqr( x^2 + ( y - 2)^2) = y - (-2) Squaring both sides:

x^2 + (y - 2)^2 = (y + 2)^2

x^2 + y^2 - 4y + 4 = y^2 + 4y + 4

x^2 - 8y = 0

x^2 = 8y

y = `1/8x^2 (answer).

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