Question

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 1

ANSWER

D. Ellipse;

$3{x}^{2} +{y}^{2} + 6x - 6y + 3= 0$

EXPLANATION

The given equation is

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

Dividing through by 9 gives

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

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

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

We multiply through by 9 to get,

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

Expand to obtain;

$3( {x}^{2} + 2x + 1) + {y}^{2} - 6y + 9 = 9$

Expand to obtain;

$3{x}^{2} + 6x + 3+ {y}^{2} - 6y + 9 = 9$

Regroup and equate to zero to obtain;

$3{x}^{2} +{y}^{2} + 6x - 6y + 3= 0$

Answer 2

Answer:

ANSWER

D. Ellipse;

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