What is 1/2 x+1/3 yy=3y ?

The solution to 1/2 x+1/3 yy=3y is Parabola with (h,k)=(27/2 , 9/2),p=-3/8

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1/2 x+1/3 yy=3y

\frac{1}{2} x + \frac{1}{3} yy = 3 y

(h, k) = (\frac{27}{2}, \frac{9}{2}), p = - \frac{3}{8}

Solution steps

\frac{1}{2} x + \frac{1}{3} yy = 3 y

Rewrite

\frac{1}{2} x + \frac{1}{3} yy = 3 y

in the standard form

4 (- \frac{3}{8}) (x - \frac{27}{2}) = (y - \frac{9}{2})^{2}

Therefore parabola properties are:

(h, k) = (\frac{27}{2}, \frac{9}{2}), p = - \frac{3}{8}

y^{2} - 2 x = 5

x^{2} + 4 x + 8 y + 44 = 0

4 x^{2} + 40 x + 106 + y = 0

x^{2} + y - 2 = 0

y^{2} = 6 (x + 2)

What is 1/2 x+1/3 yy=3y ?
The solution to 1/2 x+1/3 yy=3y is Parabola with (h,k)=(27/2 , 9/2),p=-3/8