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  • A hyperbola has its axis along the coordinate axes. It passes through the point (2,-1) and its conjugate axis is 10. its eccentricity isOptio

A hyperbola has its axis along the coordinate axes. It passes

through the point (2,-1) and its conjugate axis is 10. its

eccentricity is

Option: 1

\mathrm{\frac{5}{2}}


Option: 2

\mathrm{\sqrt{\frac{15}{2}}}


Option: 3

\mathrm{\sqrt{\frac{15}{4}}}


Option: 4

\mathrm{\frac{7}{2}}


Answers (1)

best_answer

(b) The curve  \mathrm{\frac{x^2}{a^2}-\frac{y^2}{b^2}=1 }  passes through (2,-1)

\mathrm{\therefore \frac{4}{a^2}-\frac{1}{b^2}=1}

conjugate axis, \mathrm{2 b=10 \Rightarrow b=5}

\mathrm{\begin{aligned} & \therefore \frac{4}{a^2}=1+\frac{1}{25}=\frac{26}{25} \Rightarrow a^2=\frac{50}{13} \\ & \text { and } e=\sqrt{1+\left(\frac{b}{a}\right)^2}=\sqrt{1+\frac{25}{50} \times 13}=\sqrt{\frac{15}{2}} \end{aligned}}

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shivangi.shekhar

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