What is 4x^2+16x-9y^2+18y=29 ?

The solution to 4x^2+16x-9y^2+18y=29 is Hyperbola with (h,k)=(-2,1),a=3,b=2

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4x^2+16x-9y^2+18y=29

4 x^{2} + 16 x - 9 y^{2} + 18 y = 29

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

Solution steps

4 x^{2} + 16 x - 9 y^{2} + 18 y = 29

Rewrite

4 x^{2} + 16 x - 9 y^{2} + 18 y = 29

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

x^{2} - 4 x - 2 y^{2} = 0

3 y^{2} - x^{2} + 18 y - 4 x + 20 = 0

9 y^{2} - x^{2} = 81

\frac{( y + 2 ) ^{2}}{3 ^{2}} - \frac{( x - 5 ) ^{2}}{5 ^{2}} = 1

x^{2} - y^{2} + 4 x + 16 y - 69 = 0

What is 4x^2+16x-9y^2+18y=29 ?
The solution to 4x^2+16x-9y^2+18y=29 is Hyperbola with (h,k)=(-2,1),a=3,b=2