Question

Write 36x^2-360x-25y^2-100y=100 in standard form. Then state whether the graphs of the equation is a parabola, circle, ellipse, or hyperbola.

I started with:
36(x^2 -10x+25)-25(y^2+4y+4)=100+36(25)-25(4)

which leads to: 36(x^2-10x+25)/900 - 25(y^2+4y+4)/900=1

Simplified to: (x-5)^2/25 - (y+2)^2/36; ellipse.

Is this correct?

Answer 1

Yes.

Answer 2

Algebra is correct, but this is then a hyperbola.

Also, try to solve more complicated problems containing a term proportional to xy, e.g.:

x^2 + 3 x + y^2 - 12 y + 15 x y = 1588

Answer 3

Yes, it's a hyperbola. I overlooked that - sign.