Question #f0d1e

1 Answer
Roella W.
Mar 17, 2016

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.

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