What is 3(x-1)^2=6+2(y+1)^2 ?

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

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3(x-1)^2=6+2(y+1)^2

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

(h, k) = (1, - 1), a = 2, b = 3

Solution steps

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

Rewrite

3 (x - 1)^{2} - 6 - 2 (y + 1)^{2} = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, - 1), a = 2, b = 3

(x - 5)^{2} - (y - 4)^{2} = 25

x^{2} - 3 y^{2} = 4

x^{2} - y^{2} = - 7

x^{2} - y^{2} = - 8

6 x^{2} - 8 y^{2} - 108 x - 64 y = - 310

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