What is (p(x)}{x/2+\frac{x-4)/3}=(3x)/4-1 ?

The solution to (p(x)}{x/2+\frac{x-4)/3}=(3x)/4-1 is Parabola with (h,k)=(22/15 ,-1/90),p= 2/5

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(p(x)}{x/2+\frac{x-4)/3}=(3x)/4-1

\frac{p ( x )}{\frac{x}{2} + \frac{x - 4}{3}} = \frac{3 x}{4} - 1

(h, k) = (\frac{22}{15}, - \frac{1}{90}), p = \frac{2}{5}

Solution steps

\frac{y}{\frac{x}{2} + \frac{x - 4}{3}} = \frac{3 x}{4} - 1

Rewrite

\frac{y}{\frac{x}{2} + \frac{x - 4}{3}} - \frac{3 x}{4} + 1 = 0

in the standard form

4 \cdot \frac{2}{5} (y - (- \frac{1}{90})) = (x - \frac{22}{15})^{2}

Therefore parabola properties are:

(h, k) = (\frac{22}{15}, - \frac{1}{90}), p = \frac{2}{5}

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

y^{2} + 8 y + 20 x + 56 = 0

y^{2} + 10 x = 0

x^{2} + 8 x - 10 y = - 4

y < x^{2}

What is (p(x)}{x/2+\frac{x-4)/3}=(3x)/4-1 ?
The solution to (p(x)}{x/2+\frac{x-4)/3}=(3x)/4-1 is Parabola with (h,k)=(22/15 ,-1/90),p= 2/5