Question

Q1: Identify the graph of the equation and write an equation of the translated or rotated graph in general form.

Answer 1

Answer:

C. hyperbola; $9x^2-25y^2-250y-850=0$

Step-by-step explanation:

The given conic has equation:

$9x^2-25y^2=225$

Divide through by 225.

$\frac{9x^2}{225}-\frac{25y^2}{225}=\frac{225}{225}$

$\frac{x^2}{25}-\frac{y^2}{9}=1$

This is a hyperbola centered at the origin.

The hyperbola has been translated from the origin to (0,5).

The translated hyperbola will have equation;

$\frac{(x-0)^2}{25}-\frac{(y-5)^2}{9}=1$

Multiply through by 225.

$9(x-0)^2-25(y-5)^2=225$

Expand

$9x^2-25(y^2-10y+25)=225$

$9x^2-25y^2+250y-625=225$

Rewrite in general form;

$9x^2-25y^2+250y-625-225=0$

$9x^2-25y^2+250y-850=0$