precal

complete the square to identify what type of conic you have, identify the key parts indicated and then graph conic.

parabola: vertex,focus, directrix, focal diameter.
ellipse: center,vertices, foci, eccentricity.
hyperbola: center, vertices, foci, slope of asymptotes.

9x^2+36=y^2+36x+6y

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  1. 9x^2+36=y^2+36x+6y
    9x^2-36x -y^2-6y = -36
    9(x^2-4x) - (y^2+6y) = -36
    9(x^2-4x+4) - (y^2+6y+9) = -36 + 9*4 - 9
    9(x-2)^2 - (y+3)^2 = -9
    (y+3)^2 - 9(x-2)^2 = 9
    (y+3)^2/9 - (x-2)^2 = 1

    That's a standard form, so you should be able to provide its description now.

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