What is 1/8 z^2-1/4 y-1=0 ?

The solution to 1/8 z^2-1/4 y-1=0 is Parabola with (h,k)=(0,-4),p= 1/2

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1/8 z^2-1/4 y-1=0

\frac{1}{8} z^{2} - \frac{1}{4} y - 1 = 0

(h, k) = (0, - 4), p = \frac{1}{2}

Solution steps

\frac{1}{8} z^{2} - \frac{1}{4} y - 1 = 0

Rewrite

\frac{1}{8} z^{2} - \frac{1}{4} y - 1 = 0

in the standard form:

4 \cdot \frac{1}{2} (y - (- 4)) = (z - 0)^{2}

Therefore parabola properties are:

(h, k) = (0, - 4), p = \frac{1}{2}

8 (x - 2) = (y + 3)^{2}

x = 9 - z^{2}

2 y^{2} - 16 x + 16 (y - 1) + 16 = - 2 y^{2}

(x - 2)^{2} + (y - 1) = 9

x + y^{2} = c

What is 1/8 z^2-1/4 y-1=0 ?
The solution to 1/8 z^2-1/4 y-1=0 is Parabola with (h,k)=(0,-4),p= 1/2