SOLUTION: How do you convert y= -(x^2/36)+1 to standard form

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Question 1099085: How do you convert y= -(x^2/36)+1 to standard form
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
y=+-%28x%5E2%2F36%5E%22%22%29%2B1

Multiply both sides by 36

36y=-x%5E2%2B36

Add x2 to both sides

x%5E2%2B36y=36

Add -36y to both sides:

x%5E2=-36y%2B36

Factor out -36 on the right side:

x%5E2=-36%28y-1%29

Write x as (x-0)

%28x-0%29%5E2=-36%28y-1%29

Compares to standard form with
vertical axis of symmetry x = 0,
which is the y-axis

%28x-h%29%5E2=4p%28y-k%29

vertex = (h,k) = (0,1)

4p = -36
 p = -9

p is negative, so parabola opens downward

Focus is |p| = |-9| = 9 units below vertex,
so focus is (0,-8)

Directrix is the (green) line 9 units above the vertex,
which is the horizontal line whose equation is
y = 10

 

Edwin