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= 3/(sqrt(2)),b=sqrt(2)

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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{3}{2}, b = 2

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

Therefore Hyperbola properties are:

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

4 x^{2} - 5 y^{2} + 30 y = 65

4244 - 98 y + 324 x - 49 y^{2} + 81 x^{2} = 0

- 16 x^{2} + 25 y^{2} + 64 x - 100 y - 364 = 0

5 x^{2} - 10 y^{2} - 10 = 0

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

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= 3/(sqrt(2)),b=sqrt(2)