What is (3y)/(y-4)= x/((y-4)(y-3)) ?

The solution to (3y)/(y-4)= x/((y-4)(y-3)) is Parabola with (h,k)=(-27/4 , 3/2),p= 1/12

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(3y)/(y-4)= x/((y-4)(y-3))

\frac{3 y}{y - 4} = \frac{x}{( y - 4 ) ( y - 3 )}

(h, k) = (- \frac{27}{4}, \frac{3}{2}), p = \frac{1}{12}

Solution steps

\frac{3 y}{y - 4} = \frac{x}{( y - 4 ) ( y - 3 )}

Rewrite

\frac{3 y}{y - 4} - \frac{x}{( y - 4 ) ( y - 3 )} = 0

in the standard form

4 \cdot \frac{1}{12} (x - (- \frac{27}{4})) = (y - \frac{3}{2})^{2}

Therefore parabola properties are:

(h, k) = (- \frac{27}{4}, \frac{3}{2}), p = \frac{1}{12}

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

y^{2} + x = 5

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

y^{2} - 12 y + 8 x = 0

x = 3 y - y^{2}

What is (3y)/(y-4)= x/((y-4)(y-3)) ?
The solution to (3y)/(y-4)= x/((y-4)(y-3)) is Parabola with (h,k)=(-27/4 , 3/2),p= 1/12