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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Ellipse

NDA 2022 · Mathematics · Ellipse

The centre of an ellipse is at (0,0) , major axis is on the y...

The centre of an ellipse is at (0,0)(0,0), major axis is on the yy-axis. If the ellipse passes through (3,2)(3,2) and (1,6)(1,6), then what is its eccentricity?

Options

  1. A32\frac{\sqrt{3}}{2}
  2. B3\sqrt{3}
  3. C52\frac{\sqrt{5}}{2}
  4. D5\sqrt{5}

Correct answer

A. 32\frac{\sqrt{3}}{2}

Step-by-step solution

Let equation of ellipse is x2b2+y2a2=1∴\frac{x^2}{b^2}+\frac{y^2}{a^2}=1\therefore \quad It passes through (3,2)(3,2) and (1,6)∴9b2+4a2=1(1,6)\therefore \frac{9}{b^2}+\frac{4}{a^2}=1 ...(i) 1b2+36a2=1\frac{1}{b^2}+\frac{36}{a^2}=1 ...(ii) Solving equations (i) and (ii), we get a2=40a^2=40 and b2=10b^2=10 Eccentricity of ellipse =1−b2a2=1−1040=32=\sqrt{1-\frac{b^2}{a^2}}=\sqrt{1-\frac{10}{40}}=\frac{\sqrt{3}}{2}
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