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

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

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

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

(h, k) = (3, 0), a = 1, b = 3

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (3, 0), a = 1, b = 3

\frac{- y ^{2}}{4} + \frac{z ^{2}}{4} = - \frac{3}{4}

2 x^{2} - y^{2} = 17

x^{2} - 4 y^{2} = 45

a^{2} - b^{2} = 8

x^{2} - 4 y^{2} + 2 x - 8 y - 19 = 0

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