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

16 x^{2} - y^{2} = 16

16 y^{2} - 9 x^{2} + 36 x + 96 y - 36 = 0

4 x^{2} - 25 y^{2} - 8 x - 100 y - 196 = 0

- \frac{x ^{2}}{25} + \frac{y ^{2}}{144} = 1

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