Answer
4 solutions
Work Step by Step
A hyperbola has lines that resemble the outline of an hourglass, and an ellipse is a stretched out circle (but without the formula of a circle).
Example: hyperbola with formula $x^{2}-y^{2}=1$, ellipse with formula $\frac{x^{2}}{4}+\frac{y^{2}}{9}=1$
The graph shows that these two equations intersect in four places.