SOLUTION: Use the discriminant to determine whether the equation represents a parabola, hyperbola, or an ellipse. 4x^2 - 9xy - 5y^2 + 15 = 0

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Use the discriminant to determine whether the equation represents a parabola, hyperbola, or an ellipse. 4x^2 - 9xy - 5y^2 + 15 = 0      Log On


   

Question 1136333: Use the discriminant to determine whether the equation represents a parabola, hyperbola, or
an ellipse. 4x^2 - 9xy - 5y^2 + 15 = 0
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
recall:
If b%5E2-4ac%3C0, then the equation represents an ellipse.
-A subordinate special case of this occurs when A=C+and+B=0, then the equation represents a circle.
- If b%5E2-4ac=0, then the equation represents a+parabola.
- If b%5E2-4ac+%3E0, then the equation represents a hyperbola.
-A subordinate special case of this occurs, when A%2BC=0, then the equation represents a rectangular hyperbola.

you are given:
4x%5E2+-+9xy+-+5y%5E2+%2B+15+=+0+...rearrange the terms
+-+5y%5E2-+9xy%2B+4x%5E2%2B+15+=+0+
a=-5,
b=-9x,
c=4x%5E2%2B15
discriminant is:
b%5E2-4ac=%28-9x%29%5E2-4%2A%28-5%29%284x%5E2%2B15%29
b%5E2-4ac=81x%5E2%2B20%284x%5E2%2B15%29
b%5E2-4ac=81x%5E2%2B80x%5E2%2B300
b%5E2-4ac=161x%5E2%2B300
=> b%5E2-4ac+%3E+0 and your equation represents a hyperbola