What is 9x^2-4y^2-18x+16y-43=0 ?

The solution to 9x^2-4y^2-18x+16y-43=0 is Hyperbola with (h,k)=(1,2),a=2,b=3

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9x^2-4y^2-18x+16y-43=0

9 x^{2} - 4 y^{2} - 18 x + 16 y - 43 = 0

(h, k) = (1, 2), a = 2, b = 3

Solution steps

9 x^{2} - 4 y^{2} - 18 x + 16 y - 43 = 0

Rewrite

9 x^{2} - 4 y^{2} - 18 x + 16 y - 43 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, 2), a = 2, b = 3

16 x^{2} - 9 y^{2} - 144 = 0

\frac{( x - 4 ) ^{2}}{2} - \frac{( y - 3 ) ^{2}}{1} = 1

\frac{( y - 7 ) ^{2}}{64} - \frac{( x - 3 ) ^{2}}{16} = 1

4 y^{2} - 9 x^{2} - 36 x + 8 y - 68 = 0

x^{2} - y^{2} = 7

What is 9x^2-4y^2-18x+16y-43=0 ?
The solution to 9x^2-4y^2-18x+16y-43=0 is Hyperbola with (h,k)=(1,2),a=2,b=3