What is 9x^2-4y^2-18x+24y+45=0 ?

The solution to 9x^2-4y^2-18x+24y+45=0 is Hyperbola with (h,k)=(1,3),a=3sqrt(2),b=2sqrt(2)

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9x^2-4y^2-18x+24y+45=0

9 x^{2} - 4 y^{2} - 18 x + 24 y + 45 = 0

(h, k) = (1, 3), a = 32, b = 22

Solution steps

9 x^{2} - 4 y^{2} - 18 x + 24 y + 45 = 0

Rewrite

9 x^{2} - 4 y^{2} - 18 x + 24 y + 45 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, 3), a = 32, b = 22

\frac{y ^{2}}{25} - \frac{( x - 4 ) ^{2}}{16} = 1

x^{2} - 2 y^{2} + 6 x + 4 y + 5 = 0

\frac{y ^{2}}{b ^{2}} - \frac{x ^{2}}{a ^{2}} = 1

25 y^{2} - x^{2} - 150 y - 16 x + 109 = 0

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

What is 9x^2-4y^2-18x+24y+45=0 ?
The solution to 9x^2-4y^2-18x+24y+45=0 is Hyperbola with (h,k)=(1,3),a=3sqrt(2),b=2sqrt(2)