Question

Question #f0d1e

Answer 1

This is an ellipse with centre at `(2,3)` and foci at `sqrt(5)` either side of the centre.

Explanation:

This is the equation of an ellipse, which you can recognise by the fact the both the `x^2` and the `y^2` terms are positive. By using the completing the squares method the equation can be rearranged into a form that will give the key dimensions and points needed to draw the graph.
`x^2 -4x +y^2 - 6y +8 = 0`
`(x-2)^2 -4 +(y-3)^2 - 9 +8 = 0`
`(x-2)^2 +(y-3)^2 =5`

`(x-2)^2/5 + (y-3)^2/5 = 1`

This is an ellipse with centre at `(2,3)` and foci at `sqrt(5)` either side of the centre.