What is y^{(2)}+8y+12x-44=0 ?

The solution to y^{(2)}+8y+12x-44=0 is Parabola with (h,k)=(5,-4),p=-3

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y^{(2)}+8y+12x-44=0

y^{(2)} + 8 y + 12 x - 44 = 0

(h, k) = (5, - 4), p = - 3

Solution steps

y^{2} + 8 y + 12 x - 44 = 0

Rewrite

y^{2} + 8 y + 12 x - 44 = 0

in the standard form

4 (- 3) (x - 5) = (y - (- 4))^{2}

Therefore parabola properties are:

(h, k) = (5, - 4), p = - 3

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

\frac{1}{3} y^{2} - \frac{5}{6} y + 2 x + \frac{1}{6} = 0

x^{2} - 16 y = 0

4 x^{2} + 48 y + 12 x - 159 = 0

y - 3 x^{2} + 10 x = 5

What is y^{(2)}+8y+12x-44=0 ?
The solution to y^{(2)}+8y+12x-44=0 is Parabola with (h,k)=(5,-4),p=-3