What is 9x^2-y^2-54x+45=0 ?

The solution to 9x^2-y^2-54x+45=0 is Hyperbola with (h,k)=(3,0),a=2,b=6

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9x^2-y^2-54x+45=0

9 x^{2} - y^{2} - 54 x + 45 = 0

(h, k) = (3, 0), a = 2, b = 6

Solution steps

9 x^{2} - y^{2} - 54 x + 45 = 0

Rewrite

9 x^{2} - y^{2} - 54 x + 45 = 0

in the form of a standard hyperbola equation

\frac{( x - 3 ) ^{2}}{2 ^{2}} - \frac{( y - 0 ) ^{2}}{6 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (3, 0), a = 2, b = 6

3 y^{2} - 4 x^{2} - 6 y - 24 x - 105 = 0

\frac{y ^{2}}{36} - \frac{x ^{2}}{13} = 1

x, 4 k (x)^{2} - 4 x (x + 1) = 7

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

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

What is 9x^2-y^2-54x+45=0 ?
The solution to 9x^2-y^2-54x+45=0 is Hyperbola with (h,k)=(3,0),a=2,b=6