Parabolas

This week, we learned about parabolas. There are two major types of parabolas: vertical and horizontal. Here are the equations for these parabolas:

Vertical:	(x – h)2 = 4p(y – k)
Horizontal:	(y – k)2 = 4p(x – h)

The vertex of the parabola is given by (h, k), and p is the distance from the vertex to the focus and also the distance from the vertex to the directrix.
Here is an example of a vertical parabola:

Let us assume that h = 2 and k = 4, and focus = (2, 5).
In order to find p, we can use the fact the y-value of the focus is k + p. After substituting in k, we get the following equation:

4 + p = 5
p = 5 – 4
p = 1

That means that the vertex, directrix, focus, and equation would be the following:

Vertex:	(2, 4)
Directrix:	y = k – p = 4 – 1 = 3
Focus:	(2, 5)
Equation:	(x – 2)2 = 4(y – 4)

The next blog post will have information about ellipses!