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.
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
1 answer
1 answer