What is x-3=(y^2+9)/(x+3) ?

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

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x-3=(y^2+9)/(x+3)

x - 3 = \frac{y ^{2} + 9}{x + 3}

(h, k) = (0, 0), a = 32, b = 32

Solution steps

x - 3 = \frac{y ^{2} + 9}{x + 3}

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 32, b = 32

x^{2} - 16 y^{2} - 16 = 0

4 x^{2} - 9 y^{2} = 15

(x - 2)^{2} - (y + 3)^{2} = 13

\frac{( x - 6 ) ^{2}}{4} - \frac{( y + 6 ) ^{2}}{81} = 1

x^{2} - y^{2} - 8 x - 4 y - 61 = 0

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