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Conic Sections — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsConic Sections2 Marks
MCQ
Eccentricity of hyperbola $\frac{x^2}{ k }+\frac{y^2}{ k ^2}=1( k <0)$ is
  • A
    $\sqrt{1+k}$
  • B
    $\sqrt{1-k}$
  • C
    $\sqrt{1+\frac{1}{k}}$
  • ✓
    $\sqrt{1-\frac{1}{k}}$
✓

Answer

Correct option: D.
$\sqrt{1-\frac{1}{k}}$
(D)
$\frac{y^2}{ k ^2}-\frac{x^2}{- k }=1$
$\text { Also }, a ^2= b ^2\left( e ^2-1\right)$
$\Rightarrow- k = k ^2\left( e ^2-1\right)$
$\Rightarrow-\frac{1}{ k }= e ^2-1$
$\Rightarrow e ^2=1-\frac{1}{ k }$
$\Rightarrow e =\sqrt{1-\frac{1}{ k }}$

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