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  • The eccentricity of the hyperbola <img alt="\mathrm{\left|\sqrt{(x-3)^2+(y-2)^2}-\sqrt{(x+1)^2+(y+1)^2}\right|=1}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Cleft

The eccentricity of the hyperbola

\mathrm{\left|\sqrt{(x-3)^2+(y-2)^2}-\sqrt{(x+1)^2+(y+1)^2}\right|=1}   is

Option: 1

5


Option: 2

8


Option: 3

4


Option: 4

2


Answers (1)

best_answer

For the given equation of the hyperbola, the foci are

\mathrm{S(3,2) \text { and } S^{\prime}(-1,-1) \text {. }}

Using the definition hyperbola, \mathrm{\left|S P-S^{\prime} P\right|=2 a} , we have

\mathrm{S S^{\prime}=5 \text { and } 2 a=1 \text {. }}

Hence, eccentricity is, \mathrm{e=\frac{S S^{\prime}}{2 a}=5}.

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manish

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