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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{( x - 3 ) ^{2}}{9} - \frac{( y - 3 ) ^{2}}{16} = 1

2 x^{2} - 2 y^{2} + 3 x - 2 y - 43 = 0

\frac{30}{x + y} + \frac{54}{x - y} = 8

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

y^{2} - 5 x^{2} = 20

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