What is (y+1)^2=4+x^2 ?

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

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(y+1)^2=4+x^2

(y + 1)^{2} = 4 + x^{2}

(h, k) = (0, - 1), a = 2, b = 2

Solution steps

(y + 1)^{2} = 4 + x^{2}

Rewrite

(y + 1)^{2} - 4 - x^{2} = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, - 1), a = 2, b = 2

\frac{( x + 4 ) ^{2}}{36} - \frac{( y - 2 ) ^{2}}{16} = 1

- 64 x^{2} + 25 y^{2} - 1152 x - 350 y - 5559 = 0

5 y^{(2)} - 16 x^{(2)} - 400 = 0

x^{2} - y^{2} + 7 x + 8 y - 5 = 0

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

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