Deriving the Equation of a Parabola Given a Focus and Directrix
In this task, you will create a vertical parabola and a horizontal parabola based on the instructions provided. You will also practice
writing equations of these parabolas.
Question 1
The vertex form of the equation of a vertical parabola is given by y = 4(x - h)2 + k, where (h, k) is the vertex of the
parabola and the absolute value of p is the distance from the vertex to the focus, which is also the distance from the vertex to
the directrix. You will use the GeoGebra geometry tool to create a vertical parabola and write the vertex form of its equation.
Open GeoGebra e, and complete each step below. If you need help, follow these instructions for using GeoGebra.
Part A
Mark the focus of the parabola you are going to create at F(6,4). Draw a horizontal line that is 6 units below the focus. This line
will be the directrix of your parabola. What is the equation of the line?