What is x^2-3y^2+2x+6y-1=0 ?

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

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x^2-3y^2+2x+6y-1=0

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

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

- 25 x^{2} + 4 y^{2} = 100

\frac{( y + 10 ) ^{2}}{36} - \frac{( x - 3 ) ^{2}}{100} = 1

33 (x - 2)^{2} - 16 (y - 5)^{2} = 528

4 x^{2} - 5 y^{2} - x + 16 y - 1 = 0

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