Practice Ellipse 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 sum of the distances to two fixed points (foci) is constant. Standard form: \frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1.
Imagine pinning two ends of a loose string to a board (these are the foci), then tracing a curve with a pencil keeping the string taut. The resulting oval shape is an ellipse. A circle is just a special ellipse where both foci coincide.
Example 1
easyFind the lengths of the semi-major and semi-minor axes of the ellipse \frac{x^2}{25} + \frac{y^2}{9} = 1.
Example 2
mediumFind the foci of the ellipse \frac{x^2}{16} + \frac{y^2}{25} = 1.
Example 3
mediumWrite the equation of an ellipse centered at the origin with foci at (\pm 4, 0) and a major axis of length 10.
Example 4
hardFind the eccentricity of the ellipse \frac{(x-2)^2}{36} + \frac{(y+1)^2}{20} = 1 and describe what it tells us about the shape.