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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

9 x^{2} - 4 y^{2} + 54 x + 8 y + 78 = 0

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

x^{2} - 9 y^{2} - 4 x + 36 y - 41 = 0

- 4 x^{2} + 8 y^{2} + 10 x - 6 y - 8 = 0

25 x^{2} - 9 y^{2} - 200 x + 36 y + 139 = 0

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