What is 9y^2-4x^2-54y-8x+41=0 ?

The solution to 9y^2-4x^2-54y-8x+41=0 is Hyperbola with (h,k)=(-1,3),a=2,b=3

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9y^2-4x^2-54y-8x+41=0

9 y^{2} - 4 x^{2} - 54 y - 8 x + 41 = 0

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

Solution steps

9 y^{2} - 4 x^{2} - 54 y - 8 x + 41 = 0

Rewrite

9 y^{2} - 4 x^{2} - 54 y - 8 x + 41 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

(x - 2)^{2} - \frac{( y - 1 ) ^{2}}{4} = 11

8 x^{2} - 15 y^{2} - 120 = 0

x^{2} - y^{2} - 2 x - 10 y - 29 = 0

9 (y + 3)^{2} - 1 (x + 2)^{2} = 15

\frac{y ^{2}}{64} - \frac{x ^{2}}{16} = 1

What is 9y^2-4x^2-54y-8x+41=0 ?
The solution to 9y^2-4x^2-54y-8x+41=0 is Hyperbola with (h,k)=(-1,3),a=2,b=3