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

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

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

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

(h, k) = (4, 0), a = 2, b = 2

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (4, 0), a = 2, b = 2

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

3 (x - 2)^{(2)} - 2 (y - 2)^{(2)} = - 11

2 x^{2} - 6 y^{2} + 14 = 0

(x + y) (x - y) \geq 1

16 x^{2} - 9 y^{2} + 96 x - 72 y + 144 = 0

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