trigonometry

classify the graph of the equation -4y^2+5X+3y+7=0 as a circle, a parabola, an ellipse, or a hyperbola.

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  1. since there's y^2 but no x^2, it's a parabola, opening to the right:

    5x = 4y^2 - 3y - 7
    x = 4/5 y^2 - 3/5 y - 7/5
    x = 4/5 (y^2 - 3/4 y) - 7/5
    x = 4/5 (y^2 - 3/4 y + (3/8)^2) - 7/5 - 4/5 * (3/8)^2
    x = 4/5 (y - 3/8)^2 - 121/80

    so the vertex is at (-121/80,3/8)

    http://www.wolframalpha.com/input/?i=plot+-4y^2%2B5X%2B3y%2B7+%3D+0

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