Hi

putting equations into the standard form for the conic

completing the squares

1) parabola: x^2-2x+8y+9=0  

   (x-1)^2 = -8y - 8

   (x-1)^2 = -8(y+1)

2)parabola: x^2-2x+8y+17=0

   (x-1)^2 = -8y-16

   (x-1)2 = -8(y+2)

3)parabola: y^2-4y-4x=0

  (y-2)^2 = 4x + 4

  (y-2)^2 = 4(x+1)

4)hyperbola; 12x^2-20y^2-12x+40y-37=0 

     12[(x-.5)^2 - .25]  - 20[(y+1)^2-1] - 37 = 0

     12(x-.5)^2  -3  - 20(y+1)^2 + 20 - 37 = 0

      12(x-.5)^2 - 20(y+1)^2 = 20

        (x-.5)^2/20/12 - (y+1)^2 = 1

            

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