What is z/y-(3y-8z)/4 =2z ?

The solution to z/y-(3y-8z)/4 =2z is Parabola with (h,k)=(0,0),p= 1/3

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z/y-(3y-8z)/4 =2z

\frac{z}{y} - \frac{3 y - 8 z}{4} = 2 z

(h, k) = (0, 0), p = \frac{1}{3}

Solution steps

\frac{z}{y} - \frac{3 y - 8 z}{4} = 2 z

Rewrite

\frac{z}{y} - \frac{3 y - 8 z}{4} - 2 z = 0

in the standard form

4 \cdot \frac{1}{3} (z - 0) = (y - 0)^{2}

Therefore parabola properties are:

(h, k) = (0, 0), p = \frac{1}{3}

y^{2} + 2 x = 3

x^{2} - 2 x - y = 6

y^{2} = 5 x - 9

x = 3 y^{2} - 8

- 12 x + 24 y^{2} = 0

What is z/y-(3y-8z)/4 =2z ?
The solution to z/y-(3y-8z)/4 =2z is Parabola with (h,k)=(0,0),p= 1/3