What is -4x^2+9y^2-24x-54y+81=0 ?

The solution to -4x^2+9y^2-24x-54y+81=0 is Hyperbola with (h,k)=(-3,3),a=3,b=2

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-4x^2+9y^2-24x-54y+81=0

- 4 x^{2} + 9 y^{2} - 24 x - 54 y + 81 = 0

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

Solution steps

- 4 x^{2} + 9 y^{2} - 24 x - 54 y + 81 = 0

Rewrite

- 4 x^{2} + 9 y^{2} - 24 x - 54 y + 81 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

4 x^{(2)} - 9 y^{(2)} = 216

\frac{( y + 2 ) ^{2}}{9} - \frac{( x - 3 ) ^{2}}{16} = 1

f (x) \cdot f (x) = 2 x^{2} - x - 10

\frac{y ^{2}}{100} - \frac{( x - 2 ) ^{2}}{64} = 1

\frac{x ^{2}}{16} - \frac{( y + 6 ) ^{2}}{9} = 1

What is -4x^2+9y^2-24x-54y+81=0 ?
The solution to -4x^2+9y^2-24x-54y+81=0 is Hyperbola with (h,k)=(-3,3),a=3,b=2