I am supposed to write the standard equation of the parabola with the directrix x=1, and the vertex 6,2. I got y-6=1/4p(x-2)^2. Is this correct?

I am supposed to graph y+3=-1/12(x-1)^2. I tried to find p, and I got 36. I don't think this could be correct, because the graph I am given does not have that high of a range. THe graph almost forms your traditional cross, with just a little bit of space in the positive quadrants, and a lot of space in the negative quadrants. What is the real definition of p? How do you find that? Then what is the focus and the directrix from p? Thanks

1 answer

I'll answer the first question.

The directrix is vertical so the parabola opens sideways. The equation is therefore of the form:

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

The directed distance from the directrix to the vertex is p.

p = 6 - 1 = 5
4p = 4*5 = 20

p is positive so the parabola opens to the right.

The equation of the parabola is therefore:

4p(x - h) = (y - k)^2
20(x - 6) = (y - 2)^2