What is y^{(2)}+8x+2y+33=0 ?

The solution to y^{(2)}+8x+2y+33=0 is Parabola with (h,k)=(-4,-1),p=-2

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y^{(2)}+8x+2y+33=0

y^{(2)} + 8 x + 2 y + 33 = 0

(h, k) = (- 4, - 1), p = - 2

Solution steps

y^{2} + 8 x + 2 y + 33 = 0

Rewrite

y^{2} + 8 x + 2 y + 33 = 0

in the standard form

4 (- 2) (x - (- 4)) = (y - (- 1))^{2}

Therefore parabola properties are:

(h, k) = (- 4, - 1), p = - 2

x^{2} - 4 x - 12 y - 8 = 0

x^{2} + 5 y = 14 x + 11

- 3 x^{2} + 42 x - y = 0

y^{2} = 5 y + 7 x

x = 3 (y + 1)^{2} + 5

What is y^{(2)}+8x+2y+33=0 ?
The solution to y^{(2)}+8x+2y+33=0 is Parabola with (h,k)=(-4,-1),p=-2