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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Ellipse

NTA Abhyas 2020 · Mathematics · Ellipse

Variable ellipses are drawn with x = - 4 as directrix and the...

Variable ellipses are drawn with x=−4x = - 4 as directrix and the origin as the corresponding focus. The eccentricity of the locus of the extremities of the minor axes of these ellipses isVariable ellipses are drawn with x = - 4 as directrix and the origin as the corresponding focus. The eccentricity of

Options

  1. A11
  2. B22
  3. C2\sqrt{2}
  4. D12\dfrac{1}{2}

Correct answer

A. 11

Step-by-step solution

Variable ellipses are drawn with x = - 4 as directrix and the origin as the corresponding focus. The eccentricity of
Now k=bk = b and h=aeh = ae
Also ae−ae=4⇒a(1−e2)=4e\dfrac{a}{e} - ae = 4 ⇒ a\left(1 - e^{2}\right) = 4e
⇒a2(1−e2)=4ae⇒ a^{2}\left(1 - e^{2}\right) = 4ae
⇒b2=4h⇒ b^{2} = 4h
⇒k2=4h⇒⇒ k^{2} = 4h ⇒y2=4x\begin{array}{ll}y^{2} = 4x\end{array}$<br/><br />⇒eccentricityeccentricity= 1$
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