Question #f0d1e

1 Answer
Mar 17, 2016

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

Explanation:

This is the equation of an ellipse, which you can recognise by the fact the both the x2 and the y2 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.
x24x+y26y+8=0
(x2)24+(y3)29+8=0
(x2)2+(y3)2=5

(x2)25+(y3)25=1

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