What is 4x^2+8x-y^2+2y=-5 ?

The solution to 4x^2+8x-y^2+2y=-5 is Hyperbola with (h,k)=(-1,1),a=sqrt(2),b=sqrt(1/2)

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4x^2+8x-y^2+2y=-5

4 x^{2} + 8 x - y^{2} + 2 y = - 5

(h, k) = (- 1, 1), a = 2, b = \frac{1}{2}

Solution steps

4 x^{2} + 8 x - y^{2} + 2 y = - 5

Rewrite

4 x^{2} + 8 x - y^{2} + 2 y = - 5

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 1, 1), a = 2, b = \frac{1}{2}

\frac{( y + 5 ) ^{2}}{25} - \frac{( x - 6 ) ^{2}}{16} = 1

2 x^{2} - 3 y^{2} = 15

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

(x - 9)^{2} - 9 (y + 7)^{2} = 1

4 x^{2} - 9 y^{2} + 24 x - 36 y - 36 = 0

What is 4x^2+8x-y^2+2y=-5 ?
The solution to 4x^2+8x-y^2+2y=-5 is Hyperbola with (h,k)=(-1,1),a=sqrt(2),b=sqrt(1/2)