What is 3x^2-2y^2+6x+4=0 ?

The solution to 3x^2-2y^2+6x+4=0 is Hyperbola with (h,k)=(-1,0),a=sqrt(1/2),b=sqrt(1/3)

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3x^2-2y^2+6x+4=0

3 x^{2} - 2 y^{2} + 6 x + 4 = 0

(h, k) = (- 1, 0), a = \frac{1}{2}, b = \frac{1}{3}

Solution steps

3 x^{2} - 2 y^{2} + 6 x + 4 = 0

Rewrite

3 x^{2} - 2 y^{2} + 6 x + 4 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 1, 0), a = \frac{1}{2}, b = \frac{1}{3}

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

\frac{x ^{2}}{16 + ( y - 4 ) ^{2}} = 1

- \frac{x ^{2}}{16} + \frac{y ^{2}}{36} = 1

16 x^{2} - 9 y^{2} - 64 x + 54 y - 161 = 0

3 x^{2} - 2 y^{2} + 6 x - 8 y - 17 = 0

What is 3x^2-2y^2+6x+4=0 ?
The solution to 3x^2-2y^2+6x+4=0 is Hyperbola with (h,k)=(-1,0),a=sqrt(1/2),b=sqrt(1/3)