What is x^2-y^2+6x-9y-3=0 ?

The solution to x^2-y^2+6x-9y-3=0 is Hyperbola with (h,k)=(-3,-9/2),a=(sqrt(33))/2 ,b=(sqrt(33))/2

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x^2-y^2+6x-9y-3=0

x^{2} - y^{2} + 6 x - 9 y - 3 = 0

(h, k) = (- 3, - \frac{9}{2}), a = \frac{33}{2}, b = \frac{33}{2}

Solution steps

x^{2} - y^{2} + 6 x - 9 y - 3 = 0

Rewrite

x^{2} - y^{2} + 6 x - 9 y - 3 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - \frac{9}{2} ) ) ^{2}}{( \frac{33}{2} ) ^{2}} - \frac{( x - ( - 3 ) ) ^{2}}{( \frac{33}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 3, - \frac{9}{2}), a = \frac{33}{2}, b = \frac{33}{2}

3 x^{2} - 6 x - 4 y^{2} - 9 = 0

9 x^{2} - 4 y^{2} - 18 x - 16 y = 43

5 x^{2} - 3 y^{2} + 35 x + 24 y + 25 = 0

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

\frac{y ^{2}}{9} - \frac{x ^{2}}{7} = 1

What is x^2-y^2+6x-9y-3=0 ?
The solution to x^2-y^2+6x-9y-3=0 is Hyperbola with (h,k)=(-3,-9/2),a=(sqrt(33))/2 ,b=(sqrt(33))/2