What is 4x^2-9y^2-16x+18y+11=0 ?

The solution to 4x^2-9y^2-16x+18y+11=0 is Hyperbola with (h,k)=(2,1),a= 2/3 ,b=1

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4x^2-9y^2-16x+18y+11=0

4 x^{2} - 9 y^{2} - 16 x + 18 y + 11 = 0

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

Solution steps

4 x^{2} - 9 y^{2} - 16 x + 18 y + 11 = 0

Rewrite

4 x^{2} - 9 y^{2} - 16 x + 18 y + 11 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{( y + 1 ) ^{2}}{9} - \frac{( x + 3 ) ^{2}}{4} = 1

16 x^{2} - 64 x - 9 y^{2} - 54 y + 1 = 0

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

7 x^{2} - 9 y^{2} - 63 = 0

9 y^{2} - 4 x^{2} - 8 x - 12 y + 16 = 0

What is 4x^2-9y^2-16x+18y+11=0 ?
The solution to 4x^2-9y^2-16x+18y+11=0 is Hyperbola with (h,k)=(2,1),a= 2/3 ,b=1