# How do use the discriminant test to determine whether the graph #4x^2-8xy+6y^2+10x-2y-20=0# whether the graph is parabola, ellipse, or hyperbola?

##### 1 Answer

Dec 31, 2016

See the classification, in the explanation.

#### Explanation:

graph{4x^2-8xy+6y^2+10x-2y-20=0 [-20, 20, -10, 10]}

second degree

represents a real circle, if

The graph is a pair of straight lines, if

Failing these tests, the graph is

an ellipse, if

a parabola, if

D = 0

and a hyperbola, if

Here, the equation is

The graph ( if not a pair of straight lines ) is an ellipse.

See the Socratic graph for the ellipse