What is x^2+2y-2x+8y+5=0 ?

The solution to x^2+2y-2x+8y+5=0 is Parabola with (h,k)=(1,-2/5),p=-5/2

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x^2+2y-2x+8y+5=0

x^{2} + 2 y - 2 x + 8 y + 5 = 0

(h, k) = (1, - \frac{2}{5}), p = - \frac{5}{2}

Solution steps

x^{2} + 2 y - 2 x + 8 y + 5 = 0

Rewrite

x^{2} + 2 y - 2 x + 8 y + 5 = 0

in the standard form

4 (- \frac{5}{2}) (y - (- \frac{2}{5})) = (x - 1)^{2}

Therefore parabola properties are:

(h, k) = (1, - \frac{2}{5}), p = - \frac{5}{2}

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

y = \frac{2 x}{y}

x^{2} - 2 y = 7

y = - \frac{1}{2} (x + 1)^{2} + 5

y^{2} = 14 x

What is x^2+2y-2x+8y+5=0 ?
The solution to x^2+2y-2x+8y+5=0 is Parabola with (h,k)=(1,-2/5),p=-5/2