What is 9x^2-y^2+54x+10y+55=0 ?

The solution to 9x^2-y^2+54x+10y+55=0 is Hyperbola with (h,k)=(-3,5),a= 1/3 ,b=1

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9x^2-y^2+54x+10y+55=0

9 x^{2} - y^{2} + 54 x + 10 y + 55 = 0

(h, k) = (- 3, 5), a = \frac{1}{3}, b = 1

Solution steps

9 x^{2} - y^{2} + 54 x + 10 y + 55 = 0

Rewrite

9 x^{2} - y^{2} + 54 x + 10 y + 55 = 0

in the form of a standard hyperbola equation

\frac{( x - ( - 3 ) ) ^{2}}{( \frac{1}{3} ) ^{2}} - \frac{( y - 5 ) ^{2}}{1 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 3, 5), a = \frac{1}{3}, b = 1

4 x^{(2)} - 25 y^{(2)} + 16 x + 50 y - 109 = 0

x^{2} + 12 = y^{2} + 6 x - 2 y

- 36 x^{2} + 25 y^{2} = 900

\frac{y ^{2}}{12} - \frac{x ^{2}}{4} = 1

\frac{16 y ^{2}}{1} - \frac{25 x ^{2}}{1} = 1

What is 9x^2-y^2+54x+10y+55=0 ?
The solution to 9x^2-y^2+54x+10y+55=0 is Hyperbola with (h,k)=(-3,5),a= 1/3 ,b=1