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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

x^{2} - y^{2} \leq 16

x^{2} + 25 = y^{2}

x^{2} - y^{2} - 2 x - y + 1 = 0

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

4 x^{2} - 25 (y - 1)^{2} = 100

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