What is (y+1)^2-x^2=8 ?

The solution to (y+1)^2-x^2=8 is Hyperbola with (h,k)=(0,-1),a=2sqrt(2),b=2sqrt(2)

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(y+1)^2-x^2=8

(y + 1)^{2} - x^{2} = 8

(h, k) = (0, - 1), a = 22, b = 22

Solution steps

(y + 1)^{2} - x^{2} = 8

Rewrite

(y + 1)^{2} - x^{2} = 8

in the form of a standard hyperbola equation

\frac{( y - ( - 1 ) ) ^{2}}{( 2 2 ) ^{2}} - \frac{( x - 0 ) ^{2}}{( 2 2 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, - 1), a = 22, b = 22

3 x^{2} - y^{2} + 18 x + 18 = 0

36 x^{2} - 25 y^{2} - 8 x - 8 y + 76 = 0

- 16 x^{2} + 9 y^{2} - 64 x - 18 y = 199

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

2 y^{2} - 3 x^{2} - 4 y + 12 x + 8 = 0

What is (y+1)^2-x^2=8 ?
The solution to (y+1)^2-x^2=8 is Hyperbola with (h,k)=(0,-1),a=2sqrt(2),b=2sqrt(2)