What is 3x^2-3y^2+x+y+1=0 ?

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

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3x^2-3y^2+x+y+1=0

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

(h, k) = (- \frac{1}{6}, \frac{1}{6}), a = \frac{1}{3}, b = \frac{1}{3}

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- \frac{1}{6}, \frac{1}{6}), a = \frac{1}{3}, b = \frac{1}{3}

- 4 x^{2} + y^{2} - 40 x - 16 = 0

x^{2} + 8 x - y^{2} - 4 y = 5

- 9 y^{2} + 9 z^{2} = 4

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

y^{2} - 2 x^{2} - 4 x - 4 y = 8

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