# Analytic Geometry

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A parabola has a directrix y=-3, axis =4 and latus rectum equal to 2. find its equation.

• Analytic Geometry -

1/a = 2.
a = 1/2.
1/4a = 1/2.

k- (-3) = 1/4a = 1/2.
k + 3 = 1/2
k = 1/2 - 6/2 = -5/2.

h = axis = 4.

Y = Y = a(x-h)^2 + k.
Y = (1/2)(x-4)^2 - 5/2.

• Analytic Geometry -

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