What is -12x^2+9y^2+24x-6y+9=0 ?

The solution to -12x^2+9y^2+24x-6y+9=0 is Hyperbola with (h,k)=(1, 1/3),a=sqrt(5/3),b=(2sqrt(5))/3

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-12x^2+9y^2+24x-6y+9=0

- 12 x^{2} + 9 y^{2} + 24 x - 6 y + 9 = 0

(h, k) = (1, \frac{1}{3}), a = \frac{5}{3}, b = \frac{2 5}{3}

Solution steps

- 12 x^{2} + 9 y^{2} + 24 x - 6 y + 9 = 0

Rewrite

- 12 x^{2} + 9 y^{2} + 24 x - 6 y + 9 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, \frac{1}{3}), a = \frac{5}{3}, b = \frac{2 5}{3}

\frac{y ^{2}}{4} - \frac{x ^{2}}{16} = 1

- \frac{( x - 3 ) ^{2}}{25} + \frac{( y - 4 ) ^{2}}{36} = 1

137 + 6 y = y^{2} - 24 x - x^{2}

\frac{y ^{2}}{25} - \frac{( x - 5 ) ^{2}}{16} = 1

4 x^{2} - y^{2} - 12 y + 36 = 0

What is -12x^2+9y^2+24x-6y+9=0 ?
The solution to -12x^2+9y^2+24x-6y+9=0 is Hyperbola with (h,k)=(1, 1/3),a=sqrt(5/3),b=(2sqrt(5))/3