What is y^2-9x^2-6y+54x=153 ?

The solution to y^2-9x^2-6y+54x=153 is Hyperbola with (h,k)=(3,3),a=9,b=3

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y^2-9x^2-6y+54x=153

y^{2} - 9 x^{2} - 6 y + 54 x = 153

(h, k) = (3, 3), a = 9, b = 3

Solution steps

y^{2} - 9 x^{2} - 6 y + 54 x = 153

Rewrite

y^{2} - 9 x^{2} - 6 y + 54 x = 153

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (3, 3), a = 9, b = 3

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

4 x^{2} - y^{2} - 24 x - 6 y + 11 = 0

9 x^{2} - 8 y^{2} = 72

- 16 x^{2} + 25 y^{2} - 160 x - 150 y - 575 = 0

x^{2} - y^{2} = \frac{2}{3}

What is y^2-9x^2-6y+54x=153 ?
The solution to y^2-9x^2-6y+54x=153 is Hyperbola with (h,k)=(3,3),a=9,b=3