Answer:
C. hyperbola; [tex]9x^2-25y^2-250y-850=0[/tex]
Step-by-step explanation:
The given conic has equation:
[tex]9x^2-25y^2=225[/tex]
Divide through by 225.
[tex]\frac{9x^2}{225}-\frac{25y^2}{225}=\frac{225}{225}[/tex]
[tex]\frac{x^2}{25}-\frac{y^2}{9}=1[/tex]
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;
[tex]\frac{(x-0)^2}{25}-\frac{(y-5)^2}{9}=1[/tex]
Multiply through by 225.
[tex]9(x-0)^2-25(y-5)^2=225[/tex]
Expand
[tex]9x^2-25(y^2-10y+25)=225[/tex]
[tex]9x^2-25y^2+250y-625=225[/tex]
Rewrite in general form;
[tex]9x^2-25y^2+250y-625-225=0[/tex]
[tex]9x^2-25y^2+250y-850=0[/tex]
