Identify the graph of 3x^2+y^2=9 for t(-1,3) and write an equation of the translated or rotated graph in general form.

ANSWER

D. Ellipse;

EXPLANATION

The given equation is

Dividing through by 9 gives

This is the equation of an ellipse centered at the origin.

If this ellipse has been translated, so that its center is now at (-1,3), then the equation of the translated ellipse becomes

We multiply through by 9 to get,

Expand to obtain;

Expand to obtain;

Regroup and equate to zero to obtain;