What is x^2+2x-y^2+6y=15 ?

The solution to x^2+2x-y^2+6y=15 is Hyperbola with (h,k)=(-1,3),a=sqrt(7),b=sqrt(7)

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x^2+2x-y^2+6y=15

x^{2} + 2 x - y^{2} + 6 y = 15

(h, k) = (- 1, 3), a = 7, b = 7

Solution steps

x^{2} + 2 x - y^{2} + 6 y = 15

Rewrite

x^{2} + 2 x - y^{2} + 6 y = 15

in the form of a standard hyperbola equation

\frac{( x - ( - 1 ) ) ^{2}}{( 7 ) ^{2}} - \frac{( y - 3 ) ^{2}}{( 7 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 1, 3), a = 7, b = 7

5 x^{2} - 4 y^{2} - 20 x + 24 y - 36 = 0

x^{2} - 2 x + 1 = 2 k (x) (k (x) - 2)

16 x^{2} - 25 y^{2} = 100

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

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

What is x^2+2x-y^2+6y=15 ?
The solution to x^2+2x-y^2+6y=15 is Hyperbola with (h,k)=(-1,3),a=sqrt(7),b=sqrt(7)