What is x^2+6x-4y^2-8y+9=0 ?

The solution to x^2+6x-4y^2-8y+9=0 is Hyperbola with (h,k)=(-3,-1),a=1,b=2

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x^2+6x-4y^2-8y+9=0

x^{2} + 6 x - 4 y^{2} - 8 y + 9 = 0

(h, k) = (- 3, - 1), a = 1, b = 2

Solution steps

x^{2} + 6 x - 4 y^{2} - 8 y + 9 = 0

Rewrite

x^{2} + 6 x - 4 y^{2} - 8 y + 9 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 3, - 1), a = 1, b = 2

y^{2} = 3 6^{2} + x^{2}

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

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

\frac{( x - 6 ) ^{2}}{4} - \frac{( y + 7 ) ^{2}}{36} = 1

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

What is x^2+6x-4y^2-8y+9=0 ?
The solution to x^2+6x-4y^2-8y+9=0 is Hyperbola with (h,k)=(-3,-1),a=1,b=2