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3 years ago

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

Mathematics

2 answers:

Gennadij [26K]3 years ago

6 0

Answer:

ellipse;

Step-by-step explanation:

MAVERICK [17]3 years ago

4 0

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

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