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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Ellipse

NDA 2023 · Mathematics · Ellipse

Paragraph: Consider the following for the next two (02) items that...

Paragraph: Consider the following for the next two (02)(02) items that follow: P(x,y)\mathrm{P}(x, y) is any point on the ellipse x2+4y2=1x^2+4 y^2=1. Let E,FE, F be the foci of the ellipse.
Question: Consider the following points: 1. (32,0)\left(\frac{\sqrt{3}}{2}, 0\right) 2. (32,14)\left(\frac{\sqrt{3}}{2}, \frac{1}{4}\right) 3. (32,−14)\left(\frac{\sqrt{3}}{2},-\frac{1}{4}\right) Which of the following points lie on latus rectum of ellipse?

Options

  1. A1 and 2 only
  2. B2 and 3 only
  3. C1 and 3 only
  4. D1,2 and 3

Correct answer

D. 1,2 and 3

Step-by-step solution

b2=a2b^2=a^2\left(1-e^2\right)\frac{1}{4}=1-e^2 \Rightarrow e=\frac{\sqrt{3}}{2}fociifocii( \pm a e, 0)= \left( \pm \frac{\sqrt{3}}{2},0\right)Equationoflatusrectum,Equation of latus rectum,x= \pm \frac{\sqrt{3}}{2}\therefore \quadAll3 points lie on latus rectum
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