What is 9x^2-y^2-18x+10y-52=0 ?

The solution to 9x^2-y^2-18x+10y-52=0 is Hyperbola with (h,k)=(1,5),a=2,b=6

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9x^2-y^2-18x+10y-52=0

9 x^{2} - y^{2} - 18 x + 10 y - 52 = 0

(h, k) = (1, 5), a = 2, b = 6

Solution steps

9 x^{2} - y^{2} - 18 x + 10 y - 52 = 0

Rewrite

9 x^{2} - y^{2} - 18 x + 10 y - 52 = 0

in the form of a standard hyperbola equation

\frac{( x - 1 ) ^{2}}{2 ^{2}} - \frac{( y - 5 ) ^{2}}{6 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (1, 5), a = 2, b = 6

- \frac{x ^{2}}{16} + \frac{y ^{2}}{9} = 1

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

x^{2} - y^{2} - 4 x - 2 y - 1 = 0

x^{2} - y^{2} + 6 x - 9 y + 81 = 0

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

What is 9x^2-y^2-18x+10y-52=0 ?
The solution to 9x^2-y^2-18x+10y-52=0 is Hyperbola with (h,k)=(1,5),a=2,b=6