Question 545209: 0=y^2-8x+4y-20 ive tried everything but i can't get the answer. its asking for the equation in standard form,vertex,focus,directrix,and the functions in terms of y.
Answer by Edwin McCravy(20059)   (Show Source):
You can put this solution on YOUR website!
The standard form is
(y-k)² = 4p(x-h)
0 = y² - 8x + 4y - 20
y² - 8x + 4y - 20 = 0
y² + 4y = 8x + 20
Multiply the coefficient of y, which is 4, by  , getting 2
Then square 2, getting 4, and add 4 to both sides:
y² + 4y + 4 = 8x + 20 + 4
(y + 2)(y + 2) = 8x + 24
(y + 2)² = 4(x + 3)
Compare to the standard form:
(y - k)² = 4p(x - h)
So the vertex is (h,k) = (-3,-2), 4p = 4, so p = 1
Since p is positive, the parabola opens right. Since p = 1,
The focus is a point 1 unit to the right of the vertex (-2,-2),
and the directrix is a vertical line 1 unit left of the vertex,
so its equation is x = -4, the green line:
Edwin
|
|
|
