Graph the equation of the translated graph in general form?

9x² - 25y² = 225 for T subscript(0, -5)

This is what I did:

9x² - 25(y + 5)² = 225

9x² - 25y² - 250y - 850 = 0

So to graph it I have to rewrite the general form equation in quadratic form, ay² + by + c = 0, and then solve for y with the quadratic formula:

(-25)y² + (-250)y + (9x² - 850) = 0

y = {250±√[(-250)² - 4(-25)(9x² - 850)]} / 2(-25)

But when I try to graph it on a calculator it doesn't work. Help please! (Worried)

Re: Graph the equation of the translated graph in general form?

Quote:

Originally Posted by

**explodingtoenails** 9x² - 25y² = 225 for T subscript(0, -5)

This is what I did:

9x² - 25(y + 5)² = 225

How did you get that?

Are you aiming for a hyperbola $\displaystyle \displaystyle \frac{x^2}{5^2}-\frac{y^2}{3^2}= 1$ ?

Re: Graph the equation of the translated graph in general form?

The + 5 came from the ordered pair (0, -5) which was the translation I had to give respect to.

And yes it is a hyperbola but the problem wanted it in general form, Ax² + Bxy + Cy² + Dx + Ey + F = 0.

Re: Graph the equation of the translated graph in general form?

Is the calculator window set correctly?

Re: Graph the equation of the translated graph in general form?

I guess not, but I have no idea what settings I should give to the window.

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Re: Graph the equation of the translated graph in general form?

$\displaystyle 9x^2 - 25y^2 = 225$ **this hyperbola** is centered at the origin.

$\displaystyle T_{(0,-5)}$ translates the hyperbola down 5 units ...

$\displaystyle 9x^2 - 25(y+5)^2 = 225$

translated hyperbola

Re: Graph the equation of the translated graph in general form?

I'm very aware that I could have done that; the issue was that the book wanted the equation in GENERAL form before graphing (Ax² + Bxy + Cy² + Dx + Ey + F = 0).

Re: Graph the equation of the translated graph in general form?

Quote:

Originally Posted by

**explodingtoenails** I'm very aware that I could have done that; the issue was that the book wanted the equation in GENERAL form before graphing (Ax² + Bxy + Cy² + Dx + Ey + F = 0).

fine, then expand the equation $\displaystyle 9x^2 - 25(y+5)^2 = 225$ after graphing ... note that the general form is not conducive to graphing.