Parabolas as Conic Sections

Each of the problems below is a link. If you click on the problem, it will take you to a YouTube video of a full, step-by-step solution for the problem. You may try these problems as practice and use the videos to check your answer, or you can just watch the videos to see more worked-out example problems.

Find the focus, directrix, and focal diameter of the parabola x squared = 4y. Then, sketch a graph of the parabola and its directrix.
Find the focus, directrix, and focal diameter of the parabola y squared = negative 6x. Then, sketch a graph of the parabola and its directrix.
Find an equation for the parabola that has its vertex at the origin and its focus at left paren 0 comma 1 right paren
Find an equation for the parabola that has its vertex at the origin and its focus at left paren negative 2 comma 0 right paren
Find an equation for the parabola that has its vertex at the origin and its directrix at x = 2
Find an equation for the parabola that has its vertex at the origin and its directrix at y = negative 1 half
A searchlight has a parabolic reflector that forms a “bowl” which is 12 inches wide from rim to rim and 8 inches deep. If the filament of the light bulb is located at the focus, how far is the filament from the vertex?
A reflector for a satellite dish is parabolic in cross-section, with the receiver at the focus. The reflector is 1 foot deep and 10 feet wide from rim to rim. How far is the receiver from the vertex?