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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

10 y^{2} - 5 x^{2} = 50

y^{2} - 3 x^{2} - 4 x - 1 = 0

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

\frac{x ^{2}}{8} - \frac{y ^{2}}{6} = 1

2 x^{2} - 4 y^{2} + 9 x - 15 y - 18 = 0

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