SOLUTION: Complete the square to determine whether the equation represents an ellipse, a parabola, a hyperbola, a degenerate conic, or results in no solution. 9x^2-6x-18y+19=0 (I alrea

Question 930952: Complete the square to determine whether the equation represents an ellipse, a parabola, a hyperbola, a degenerate conic, or results in no solution.
9x^2-6x-18y+19=0
(I already determined it is a parabola)
If it is a parabola, find the focus, vertex, and directrix.

Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
9x^2-6x= 18y-19
.......
completing the Square: 9x^2 - 6x + 0 (Format: ax^2 + bx + c)
-(-6/2*9) = 6/18 = 1/3
9(x - 1/3)^2 = 18y + -19 + 1 = 18y - 18
18y - 18 = 9(x-1/3)^2
y = (1/2)(x-1/3)^2 + 1
V(1/3,1)
1/(4p) = 1/2, p = 1/2
F(1/3, 3/2)
Directrix: y = 1/2
.......
the vertex form of a Parabola opening up(a>0) or down(a<0),

where(h,k) is the vertex and x = h is the Line of Symmetry ,
the focus is (h,k + p), With Directrix y = (k - p), a = 1/(4p)

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