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;

just took the test on edgen.

Answer 2

D. Ellipse;

`3{x}^(2) +{y}^(2) + 6x - 6y + 3= 0`

Step-by-step 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`