What is ((x-2)^2)/4-((y-1)^2)/5 =1 ?

The solution to ((x-2)^2)/4-((y-1)^2)/5 =1 is Hyperbola with (h,k)=(2,1),a=2,b=sqrt(5)

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((x-2)^2)/4-((y-1)^2)/5 =1

\frac{( x - 2 ) ^{2}}{4} - \frac{( y - 1 ) ^{2}}{5} = 1

(h, k) = (2, 1), a = 2, b = 5

Solution steps

\frac{( x - 2 ) ^{2}}{4} - \frac{( y - 1 ) ^{2}}{5} = 1

Rewrite

\frac{( x - 2 ) ^{2}}{4} - \frac{( y - 1 ) ^{2}}{5} = 1

in the form of a standard hyperbola equation

\frac{( x - 2 ) ^{2}}{2 ^{2}} - \frac{( y - 1 ) ^{2}}{( 5 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (2, 1), a = 2, b = 5

6 x^{(2)} - 5 y^{(2)} + 24 x + 20 y - 56 = 0

\frac{x ^{2}}{49} - \frac{( y + 2 ) ^{2}}{79} = 1

- \frac{x ^{2}}{144} + \frac{y ^{2}}{25} = 1

\frac{( x - 4 ) ^{2}}{16} - \frac{( y + 2 ) ^{2}}{25} = 1

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

What is ((x-2)^2)/4-((y-1)^2)/5 =1 ?
The solution to ((x-2)^2)/4-((y-1)^2)/5 =1 is Hyperbola with (h,k)=(2,1),a=2,b=sqrt(5)