Question

Q5: Identify the graph of the equation and write an equation of the translated or rotated graph in general form.

Answer 1

d.

ellipse;

Explanation:

Answer 2

`d.\:ellipse;\:3x^2+y^2+6x-6y+3=0`.

Explanation:

The given conic has equation;

`3x^2+y^2=9`

Divide through by 9.

`\Rightarrow (3x^2)/(9)+(y^2)/(9)=(9)/(9)`

`\Rightarrow (x^2)/(3)+(y^2)/(9)=1`.

This is an ellipse centered at the origin;

This ellipse has been translated so that the center is now at;

`(-1,3)`

The translated ellipse has equation;

`((x+1)^2)/(3)+((y-3)^2)/(9)=1`.

Clear the fraction;

`3(x+1)^2+(y-3)^2=9`.

Expand;

`3(x^2+2x+1)+(y^2-6y+9)=9`.

`3x^2+6x+3+y^2-6y+9=9`.

Write in general form;

`3x^2+y^2+6x-6y+9-9+3=0`.

`3x^2+y^2+6x-6y+3=0`.

The correct choice is D