What is x^{(2)}+9=y^{(2)} ?

The solution to x^{(2)}+9=y^{(2)} is Hyperbola with (h,k)=(0,0),a=3,b=3

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x^{(2)}+9=y^{(2)}

x^{(2)} + 9 = y^{(2)}

(h, k) = (0, 0), a = 3, b = 3

Solution steps

x^{2} + 9 = y^{2}

Rewrite

x^{2} + 9 = y^{2}

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 3, b = 3

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

a^{2} - b^{2} = 1

4 y^{2} - 9 x^{2} + 8 y - 54 x - 81 = 0

4 y^{2} - x^{2} - 8 y - 4 x - 4 = 0

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

What is x^{(2)}+9=y^{(2)} ?
The solution to x^{(2)}+9=y^{(2)} is Hyperbola with (h,k)=(0,0),a=3,b=3