What is 4x^2-9y^2+24x+18y-9=0 ?

The solution to 4x^2-9y^2+24x+18y-9=0 is Hyperbola with (h,k)=(-3,1),a=3,b=2

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4x^2-9y^2+24x+18y-9=0

4 x^{2} - 9 y^{2} + 24 x + 18 y - 9 = 0

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

Solution steps

4 x^{2} - 9 y^{2} + 24 x + 18 y - 9 = 0

Rewrite

4 x^{2} - 9 y^{2} + 24 x + 18 y - 9 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

2 x^{2} - 3 y^{2} < 1

x^{2} = \frac{x}{2} + y^{2}

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

\frac{( x - 0 ) ^{2}}{3 ^{2}} - \frac{( y - 0 ) ^{2}}{4 ^{2}} = 1

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

What is 4x^2-9y^2+24x+18y-9=0 ?
The solution to 4x^2-9y^2+24x+18y-9=0 is Hyperbola with (h,k)=(-3,1),a=3,b=2