What is 9x^2-4y^2+36x+8y+33=0 ?

The solution to 9x^2-4y^2+36x+8y+33=0 is Hyperbola with (h,k)=(-2,1),a= 1/2 ,b= 1/3

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9x^2-4y^2+36x+8y+33=0

9 x^{2} - 4 y^{2} + 36 x + 8 y + 33 = 0

(h, k) = (- 2, 1), a = \frac{1}{2}, b = \frac{1}{3}

Solution steps

9 x^{2} - 4 y^{2} + 36 x + 8 y + 33 = 0

Rewrite

9 x^{2} - 4 y^{2} + 36 x + 8 y + 33 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 2, 1), a = \frac{1}{2}, b = \frac{1}{3}

(x - 5)^{2} - (y - 4)^{2} = 1

144 x^{2} - 25 y^{2} + 864 x - 100 y - 2404 = 0

25 x^{2} - 16 y^{2} + 50 x + 128 y - 631 = 0

4 x^{2} - 4 y^{2} = 16

2 x^{2} - 3 y^{2} = 30

What is 9x^2-4y^2+36x+8y+33=0 ?
The solution to 9x^2-4y^2+36x+8y+33=0 is Hyperbola with (h,k)=(-2,1),a= 1/2 ,b= 1/3