SOLUTION: The equation 5x^2+4y^2=180 represents which conic section? Circle, ellipse, hyperbola or parabola?

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: The equation 5x^2+4y^2=180 represents which conic section? Circle, ellipse, hyperbola or parabola?      Log On


   



Question 742882: The equation 5x^2+4y^2=180 represents which conic section? Circle, ellipse, hyperbola or parabola?
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The equation 5x^2+4y^2=180 represents which conic section? Circle, ellipse, hyperbola or parabola?
----
Since the coefficients of x^2 and of y^2 are positive,
but not equal, it is an ellipse.
Cheers,
Stan H.
===================

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
+5x%5E2%2B4y%5E2=180
+5x%5E2%2F180%2B4y%5E2%2F180=180%2F180
+x%5E2%2F36%2By%5E2%2F45=1......it's an ellipse with center at (0,0), foci at (0,-3) and (0,3), semi-minor axis length 6, semi-major axis length 3sqrt%285%29=6.7, and vertices at (0,3sqrt%285%29) and (0,-3sqrt%285%29)