What is y 1/(2(x+1))= 1/(5(y+1)) ?

The solution to y 1/(2(x+1))= 1/(5(y+1)) is Parabola with (h,k)=(-13/8 ,-1/2),p= 1/10

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y 1/(2(x+1))= 1/(5(y+1))

y \frac{1}{2 ( x + 1 )} = \frac{1}{5 ( y + 1 )}

(h, k) = (- \frac{13}{8}, - \frac{1}{2}), p = \frac{1}{10}

Solution steps

y \frac{1}{2 ( x + 1 )} = \frac{1}{5 ( y + 1 )}

Rewrite

y \frac{1}{2 ( x + 1 )} - \frac{1}{5 ( y + 1 )} = 0

in the standard form

4 \cdot \frac{1}{10} (x - (- \frac{13}{8})) = (y - (- \frac{1}{2}))^{2}

Therefore parabola properties are:

(h, k) = (- \frac{13}{8}, - \frac{1}{2}), p = \frac{1}{10}

x = (y - 2)^{2} - 1

x^{2} + 12 x + 20 = - 8 y

(y - 1)^{2} = 4 (x + 2)

5 y = - (x - 3)^{2} - 25

x^{2} - 2 x - 8 y + 17 = 0

What is y 1/(2(x+1))= 1/(5(y+1)) ?
The solution to y 1/(2(x+1))= 1/(5(y+1)) is Parabola with (h,k)=(-13/8 ,-1/2),p= 1/10