What is z^2=(y+5)/9+5+y*(y+5)/9 ?

The solution to z^2=(y+5)/9+5+y*(y+5)/9 is Hyperbola with (h,k)=(0,-3),a=(sqrt(41))/3 ,b=sqrt(41)

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z^2=(y+5)/9+5+y*(y+5)/9

z^{2} = \frac{y + 5}{9} + 5 + y \cdot \frac{y + 5}{9}

(h, k) = (0, - 3), a = \frac{41}{3}, b = 41

Solution steps

z^{2} = \frac{y + 5}{9} + 5 + y \frac{y + 5}{9}

Rewrite

z^{2} - \frac{y + 5}{9} - 5 - y \frac{y + 5}{9} = 0

in the form of a standard hyperbola equation

\frac{( z - 0 ) ^{2}}{( \frac{41}{3} ) ^{2}} - \frac{( y - ( - 3 ) ) ^{2}}{( 41 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, - 3), a = \frac{41}{3}, b = 41

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

y^{2} - 5 x^{2} = 90

X^{2} - 4 = Y^{2}

9 x^{2} - 4 y^{2} - 18 x - 16 y - 11 = 0

x^{2} - y^{2} - 2 x - 6 y - 12 > 0

What is z^2=(y+5)/9+5+y*(y+5)/9 ?
The solution to z^2=(y+5)/9+5+y*(y+5)/9 is Hyperbola with (h,k)=(0,-3),a=(sqrt(41))/3 ,b=sqrt(41)