What is 6x^2-3y^2+12x-18y-3=0 ?

The solution to 6x^2-3y^2+12x-18y-3=0 is Hyperbola with (h,k)=(-1,-3),a=sqrt(6),b=sqrt(3)

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6x^2-3y^2+12x-18y-3=0

6 x^{2} - 3 y^{2} + 12 x - 18 y - 3 = 0

(h, k) = (- 1, - 3), a = 6, b = 3

Solution steps

6 x^{2} - 3 y^{2} + 12 x - 18 y - 3 = 0

Rewrite

6 x^{2} - 3 y^{2} + 12 x - 18 y - 3 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - 3 ) ) ^{2}}{( 6 ) ^{2}} - \frac{( x - ( - 1 ) ) ^{2}}{( 3 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 1, - 3), a = 6, b = 3

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

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

\frac{( x + 1 ) ^{2}}{25} - \frac{( y - 4 ) ^{2}}{144} = 1

2 x^{2} - 3 y^{2} = 6

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

What is 6x^2-3y^2+12x-18y-3=0 ?
The solution to 6x^2-3y^2+12x-18y-3=0 is Hyperbola with (h,k)=(-1,-3),a=sqrt(6),b=sqrt(3)