What is x^2-8x+y+8y+31=0 ?

The solution to x^2-8x+y+8y+31=0 is Parabola with (h,k)=(4,-5/3),p=-9/4

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x^2-8x+y+8y+31=0

x^{2} - 8 x + y + 8 y + 31 = 0

(h, k) = (4, - \frac{5}{3}), p = - \frac{9}{4}

Solution steps

x^{2} - 8 x + y + 8 y + 31 = 0

Rewrite

x^{2} - 8 x + y + 8 y + 31 = 0

in the standard form

4 (- \frac{9}{4}) (y - (- \frac{5}{3})) = (x - 4)^{2}

Therefore parabola properties are:

(h, k) = (4, - \frac{5}{3}), p = - \frac{9}{4}

x 4 x + 3 y = 852

y + 16 = - 2 x^{2} - 12 x

(X - 4)^{2} = 8 (Y + 6)

y \geq - x^{2} + 2 x + 3

c = z^{2} + 14

What is x^2-8x+y+8y+31=0 ?
The solution to x^2-8x+y+8y+31=0 is Parabola with (h,k)=(4,-5/3),p=-9/4