What is y/x = y/(x+15)+1/3 ?

The solution to y/x = y/(x+15)+1/3 is Parabola with (h,k)=(-15/2 ,-5/4),p= 45/4

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y/x = y/(x+15)+1/3

\frac{y}{x} = \frac{y}{x + 15} + \frac{1}{3}

(h, k) = (- \frac{15}{2}, - \frac{5}{4}), p = \frac{45}{4}

Solution steps

\frac{y}{x} = \frac{y}{x + 15} + \frac{1}{3}

Rewrite

\frac{y}{x} - \frac{y}{x + 15} - \frac{1}{3} = 0

in the standard form

4 \cdot \frac{45}{4} (y - (- \frac{5}{4})) = (x - (- \frac{15}{2}))^{2}

Therefore parabola properties are:

(h, k) = (- \frac{15}{2}, - \frac{5}{4}), p = \frac{45}{4}

y^{2} - 6 y - 12 x + 33 = 0

- 3 x^{2} + 12 x - y - 9 = 0

3 y = 21 x^{2} + 9 x + 6

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

x = 3 (y - 4)^{2}

What is y/x = y/(x+15)+1/3 ?
The solution to y/x = y/(x+15)+1/3 is Parabola with (h,k)=(-15/2 ,-5/4),p= 45/4