What is 9x^2-4y^2-18x+8y+10=0 ?

The solution to 9x^2-4y^2-18x+8y+10=0 is Hyperbola with (h,k)=(1,1),a=(sqrt(5))/2 ,b=(sqrt(5))/3

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9x^2-4y^2-18x+8y+10=0

9 x^{2} - 4 y^{2} - 18 x + 8 y + 10 = 0

(h, k) = (1, 1), a = \frac{5}{2}, b = \frac{5}{3}

Solution steps

9 x^{2} - 4 y^{2} - 18 x + 8 y + 10 = 0

Rewrite

9 x^{2} - 4 y^{2} - 18 x + 8 y + 10 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, 1), a = \frac{5}{2}, b = \frac{5}{3}

x^{2} - y^{2} - 4 x + 3 = 0

1 + y^{2} = x^{2} (\frac{10}{4})

(\frac{x ^{2}}{16}) - (\frac{( y + 4 ) ^{2}}{81}) = 1

16 x^{2} + 96 x - 9 y^{2} + 54 y + 207 = 0

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

What is 9x^2-4y^2-18x+8y+10=0 ?
The solution to 9x^2-4y^2-18x+8y+10=0 is Hyperbola with (h,k)=(1,1),a=(sqrt(5))/2 ,b=(sqrt(5))/3