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

The eccentricity ((x-1)^2)/4-((y-2)^2)/1 =1 is (sqrt(5))/2

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

eccentricity

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

\frac{5}{2}

Solution steps

= \frac{a ^{2} + b ^{2}}{a}

Calculate Hyperbola properties

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

Right-left Hyperbola with

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

= \frac{2 ^{2} + 1 ^{2}}{2}

Refine

= \frac{5}{2}

9 x^{2} - 36 x - 4 y^{2} - 24 y - 36 = 0

\frac{x ^{2}}{16} - \frac{y ^{2}}{20} = 1

16 x^{2} - 25 y^{2} = 400

16 x^{2} - 9 y^{2} = 144

4 x^{2} - y^{2} - 24 x - 4 y + 28 = 0

What is the eccentricity ((x-1)^2)/4-((y-2)^2)/1 =1 ?
The eccentricity ((x-1)^2)/4-((y-2)^2)/1 =1 is (sqrt(5))/2