Question

What is the equation of the parabola with vertex (6,7) and focus (7,7)?

Answer 1

Answer:

Step-by-step explanation:

If you plot these points on a coordinate plane, you see that they are on the same horizontal line, y = 7, with the focus 1 unit to the right of the vertex.  This means that the parabola is a sideways opening parabola, to the right, to be more specific.  That means that it has the basic vertex form

$4p(x-h)=(y-k)^2$

where p is the distance in units from the vertex to the focus, h is the first coordinate in the vertex, and k is the second coordinate in the vertex.  For us, p = 1, h = 6, and k = 7.  Now we will just fill the vertex form of the equation in with our values:

$4(x-6)=(y-7)^2$

We will solve this for x now by dividing each side by 4 and adding over the 6:

$x=\frac{1}{4}(y-7)^2+6$