What is the equation in standard form of the parabola with a focus at (3,6) and a directrix of x= 7?
First, let's analyze what we have to find what direction the parabola is facing. This will affect what our equation will be like. The directrix is x=7, meaning that the line is vertical and so will the parabola.
But which direction will it face: left or right? Well, the focus is to the left of the directrix (
(Remember that the vertex is
Let's now work on our equation! We already know the focus and directrix, but we need more. You may have noticed the letter
The focus is
How does this help us? We can find both the vertex of the graph and the scale factor using this! The vertex would be
The scale factor of this graph is shown as
Our final equation is: