SOLUTION: Identify the graph of the equation below as a parabola, an ellipse, or a hyperbola. 9x^2+8y^2-5x+8y-23=0 a. Parabola b. Hyperbola c. Ellipse

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Identify the graph of the equation below as a parabola, an ellipse, or a hyperbola. 9x^2+8y^2-5x+8y-23=0 a. Parabola b. Hyperbola c. Ellipse      Log On


   

Question 470820: Identify the graph of the equation below as a parabola, an ellipse, or a hyperbola.
9x^2+8y^2-5x+8y-23=0
a. Parabola
b. Hyperbola
c. Ellipse
Answer by Tatiana_Stebko(1539) About Me  (Show Source):
You can put this solution on YOUR website!
9x%5E2%2B8y%5E2-5x%2B8y-23=0
In the general second-degree equation Ax%5E2+%2B+Bxy+%2B+Cy%5E2+%2B+Dx+%2B+Ey+%2B+F+=+0 the discriminant B%5E2-4AC
B=0, A=9, C=8
the discriminant B%5E2-4AC=0%5E2-4%2A9%2A8=-288%3C0 if B%5E2-4AC%3C0, the equation represents an ellipse
Answer: c. Ellipse