Use the discriminant of the equation by rewriting it in the form Ax^2+Bxy+Cy^2+Dx+Ey+F=0.
Hyperbola
Practice makes perfect
We want to state whether the graph of the given equation is a parabola, a circle, an ellipse, or a hyperbola. To do so, we will rewrite it in the form Ax^2+ Bxy+ Cy^2+Dx+Ey+F=0. Then we can determine its discriminant. Recall that missing terms have coefficient 0.
5y^2+2y+4x-13x^2=81
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- 13x^2 + 0xy+ 5y^2 + 4x + 2y + (- 81)=0The discriminant of the equation can be found by evaluating B^2-4 A C. This will tell us which type of conic section we might have.
