What is x^2-2y^2+6x+4y+5=0 ?

The solution to x^2-2y^2+6x+4y+5=0 is Hyperbola with (h,k)=(-3,1),a=sqrt(2),b=1

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x^2-2y^2+6x+4y+5=0

x^{2} - 2 y^{2} + 6 x + 4 y + 5 = 0

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

Solution steps

x^{2} - 2 y^{2} + 6 x + 4 y + 5 = 0

Rewrite

x^{2} - 2 y^{2} + 6 x + 4 y + 5 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{y ^{2}}{b ^{2}} - \frac{x ^{2}}{a ^{2}} = 1

25 y^{2} - x^{2} - 150 y - 16 x + 109 = 0

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

- x^{2} + 36 y^{2} = 36

x^{2} - 4 y^{2} - 2 x - 16 y - 19 = 0

What is x^2-2y^2+6x+4y+5=0 ?
The solution to x^2-2y^2+6x+4y+5=0 is Hyperbola with (h,k)=(-3,1),a=sqrt(2),b=1