SOLUTION: 1. Find the standard form of the equation of the parabola with a focus at (0, -9) and a directrix y = 9. 2. Find the vertex, focus, directrix, and focal width of the parabola.

Algebra ->  Rational-functions -> SOLUTION: 1. Find the standard form of the equation of the parabola with a focus at (0, -9) and a directrix y = 9. 2. Find the vertex, focus, directrix, and focal width of the parabola.       Log On


   

Question 1028313: 1. Find the standard form of the equation of the parabola with a focus at (0, -9) and a directrix y = 9.
2. Find the vertex, focus, directrix, and focal width of the parabola.
x^2 = 12y
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
You can derive the equation for your question #1 using Distance Formula and the given focus and directrix and the written definition of a parabola. The previous referenced videos show how that is done.

Your question number 2 is basically in standard form and shows y as a function of x, and since coefficients are positive, this parabola has a vertex minimum and graph is concave upward. The way the equation is shown corresponds to x%5E2=4py, which can also be expanded to %28x-0%29%5E2=12%28y-0%29, telling you that vertex is at the origin, and you find p from 12=4p; and knowing p will give you information to find the focus and the directrix.