Practice Hyperbola in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The set of all points in a plane where the absolute difference of the distances to two fixed points (foci) is constant. The curve has two separate branches and asymptotes.
While an ellipse keeps the SUM of distances to foci constant, a hyperbola keeps the DIFFERENCE constant. This creates two separate curves that open away from each other, each curving toward (but never reaching) a pair of asymptotic lines.
Example 1
easyIdentify the vertices and the direction of opening for the hyperbola \frac{x^2}{9} - \frac{y^2}{16} = 1.
Example 2
mediumFind the equations of the asymptotes for the hyperbola \frac{y^2}{4} - \frac{x^2}{9} = 1.
Example 3
mediumFind the foci of the hyperbola \frac{x^2}{25} - \frac{y^2}{144} = 1.
Example 4
hardWrite the equation of the hyperbola with foci at (0, \pm 5) and vertices at (0, \pm 3).