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} - 9 y^{2} + 40 x - 72 y - 80 = 0

y^{2} = x^{2} - 9

36 x^{2} - 64 y^{2} - 504 x + 768 y - 1769 = 0

x^{2} - 4 x - y^{2} + 10 y + 5 = 0

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