SOLUTION: Derive the equation of the parabola with a focus at (2, −1) and a directrix of y = −one half. Write in standard form. I got as far as finding a by graphing the focus

Algebra ->  Rational-functions -> SOLUTION: Derive the equation of the parabola with a focus at (2, −1) and a directrix of y = −one half. Write in standard form. I got as far as finding a by graphing the focus      Log On


   

Question 878926: Derive the equation of the parabola with a focus at (2, −1) and a directrix of y = −one half. Write in standard form.
I got as far as finding a by graphing the focus and directrix to find the vertex then I found the focal length. Which is .25=p and by putting it into the equation for a=1/(4p. So I know a is equal to one but I am having trouble figuring out how to do the rest of the problem.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
focus at (2, −1) and a directrix of y = -1/2
This tells us the parabola opens downward as directrix is above focus
also tells us the V(2, -3/4) %28-1-1%2F2%29%2F2+=+-3%2F4 where p = -1/4
a = 1/(4p), a = 1/(4(-1/4)) = -1
y=+-%28x-2%29%5E2+-3%2F4 is the Vertex form, Standard Form is %28x-2%29%5E2+=+-%28y%2B3%2F4%29
the vertex form of a Parabola opening up(a>0) or down(a<0), y=a%28x-h%29%5E2+%2Bk
where(h,k) is the vertex and x = h is the Line of Symmetry
a = 1/(4p), where the focus is (h,k + p)and Directrix y = (k - p)