What is (x-4)^2-2/3 =6y-12 ?

The solution to (x-4)^2-2/3 =6y-12 is Parabola with (h,k)=(4, 17/9),p= 3/2

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(x-4)^2-2/3 =6y-12

(x - 4)^{2} - \frac{2}{3} = 6 y - 12

(h, k) = (4, \frac{17}{9}), p = \frac{3}{2}

Solution steps

(x - 4)^{2} - \frac{2}{3} = 6 y - 12

Rewrite

(x - 4)^{2} - \frac{2}{3} = 6 y - 12

in the standard form:

4 \cdot \frac{3}{2} (y - \frac{17}{9}) = (x - 4)^{2}

Therefore parabola properties are:

(h, k) = (4, \frac{17}{9}), p = \frac{3}{2}

x = 10 y^{2}

y^{2} - 8 y = 20 x - 4^{2}

y^{2} = 8 (x + 1)

x^{2} + 8 k (x) + 2 x + 2 = 0

4 x^{2} - 4 x - 8 y + 9 = 0

What is (x-4)^2-2/3 =6y-12 ?
The solution to (x-4)^2-2/3 =6y-12 is Parabola with (h,k)=(4, 17/9),p= 3/2