Question

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

Answer 1

Answer:

d.

ellipse;

Step-by-step explanation:

Answer 2

Answer:

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

Step-by-step explanation:

The given conic has equation;

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

Divide through by 9.

$\Rightarrow \frac{3x^2}{9}+\frac{y^2}{9}=\frac{9}{9}$

$\Rightarrow \frac{x^2}{3}+\frac{y^2}{9}=1$.

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;

$\frac{(x+1)^2}{3}+\frac{(y-3)^2}{9}=1$.

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