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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

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

(x + y) (x - y) = 1

\frac{( y + 2 ) ^{2}}{9} - \frac{( x + 2 ) ^{2}}{4} = 1

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

\frac{x ^{2}}{14} - \frac{y ^{2}}{20} = 1

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