What is 3x^2-y^2+6x-12y=0 ?

The solution to 3x^2-y^2+6x-12y=0 is Hyperbola with (h,k)=(-1,-6),a=sqrt(33),b=sqrt(11)

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3x^2-y^2+6x-12y=0

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

(h, k) = (- 1, - 6), a = 33, b = 11

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( y - ( - 6 ) ) ^{2}}{( 33 ) ^{2}} - \frac{( x - ( - 1 ) ) ^{2}}{( 11 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 1, - 6), a = 33, b = 11

x^{2} - 2 y^{2} \leq 3

2 x^{2} - y^{2} + 12 x - 8 y + 3 = 0

\frac{( x + 3 ) ^{2}}{4} - \frac{( y - 1 ) ^{2}}{5} = 1

16 y^{(2)} - x^{(2)} + 2 x + 64 y - 1 = 0

(\frac{x}{7})^{2} - (\frac{y}{9})^{2} = 1

What is 3x^2-y^2+6x-12y=0 ?
The solution to 3x^2-y^2+6x-12y=0 is Hyperbola with (h,k)=(-1,-6),a=sqrt(33),b=sqrt(11)