How do you find the equation of the parabola whose focus is at (3, 3) and whose directrix is at x = 7?

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Answer 1 · 2018-03-13T23:06:37

#-8(x-5)=(y-3)^2#

A quadratic relation (or function) can be in the form:

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

Since our diretrix is a vertical line, our parabola is horizontal.

We, therefore, use the form #4p(x-h)=(y-k)^2#

In this form, the focus is at #(h+p,k)# and the diretrix is at #x=h-p#

Using our information, the focus is at #(3,3)# and the diretrix is at #x=7#.

Therefore, #k=3#, #h+p=3#, and #h-p=7#

We add the second and the third equations to get:

#2h=10#

#=>h=5# You could use this to find that #p=-2#

Let's plug in what we know:

#4*-2(x-5)=(y-3)^2#

#=>-8(x-5)=(y-3)^2#