Find the particular equation with focus at origin with directrix y=3 and eccentricity of 2. I got x^2-3y^2+24y-36=0 But my book says 3y^2+16y-16=0

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Tony -If the eccentricity is greater than 1, it MUST be a hyperbola.  Your equation is a hyperbola. The book answer is simply a parabola (e=1), which must be wrong since e=2.Hope that helps