What is 9(x^2-2x)-4(y^2+4y)=-29 ?

The solution to 9(x^2-2x)-4(y^2+4y)=-29 is Hyperbola with (h,k)=(1,-2),a=3,b=2

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9(x^2-2x)-4(y^2+4y)=-29

9 (x^{2} - 2 x) - 4 (y^{2} + 4 y) = - 29

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

Solution steps

9 (x^{2} - 2 x) - 4 (y^{2} + 4 y) = - 29

Rewrite

9 (x^{2} - 2 x) - 4 (y^{2} + 4 y) = - 29

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{( y - 9 ) ^{2}}{45} - \frac{( x + 3 ) ^{2}}{\frac{45}{2}} = 1

y^{(2)} - x^{(2)} = 100

4 x^{2} - 9 y^{2} - 36 y = 72

3 x^{2} + 2 x - 3 y^{2} + 14 y = - 24

x, K (x)^{2} = 4 (128 x + x^{2})

What is 9(x^2-2x)-4(y^2+4y)=-29 ?
The solution to 9(x^2-2x)-4(y^2+4y)=-29 is Hyperbola with (h,k)=(1,-2),a=3,b=2