Practice Parabola (Focus-Directrix Definition) in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A parabola is the set of all points equidistant from a fixed point (the focus) and a fixed line (the directrix).
Every point on a parabola is exactly the same distance from the focus as it is from the directrix line. This geometric property is why satellite dishes and flashlight reflectors are parabolic—signals from the focus reflect off the curve in parallel lines.
Example 1
easyFind the focus and directrix of the parabola y = \frac{1}{8}x^2.
Example 2
mediumWrite the equation of a parabola with vertex at the origin, opening to the right, with focus at (3, 0).
Example 3
mediumFind the focus and directrix of the parabola y = \frac{1}{8}x^2.
Example 4
mediumFind the equation of the parabola with focus (0, -4) and directrix y = 4.
Example 5
hardA parabola has vertex (2, -1) and focus (2, 3). Find its equation and the length of the latus rectum.