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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Ellipse

NDA 2013 · Mathematics · Ellipse

The equation of the ellipse whose vertices are at ( ± 5,0) and foci...

The equation of the ellipse whose vertices are at (±5,0)( \pm 5,0) and foci at (±4,0)( \pm 4,0) is

Options

  1. Ax225+y29=1\frac{x^2}{25}+\frac{y^2}{9}=1
  2. Bx29+y225=1\frac{x^2}{9}+\frac{y^2}{25}=1
  3. Cx216+y225=1\frac{x^2}{16}+\frac{y^2}{25}=1
  4. Dx225+y216=1\frac{x^2}{25}+\frac{y^2}{16}=1

Correct answer

A. x225+y29=1\frac{x^2}{25}+\frac{y^2}{9}=1

Step-by-step solution

a=5 and ae=4e=45\begin{aligned} & a=5 \text{ and } a e=4 \\ & e=\frac{4}{5}\end{aligned}e2=1−b2a21625=1−b225\begin{aligned} & e^2=1-\frac{b^2}{a^2} \\ & \frac{16}{25}=1-\frac{b^2}{25}\end{aligned}⇒b225=925⇒b2=9x225+y29=1\begin{aligned} & \Rightarrow \frac{b^2}{25}=\frac{9}{25} \quad \Rightarrow b^2=9 \\ & \frac{x^2}{25}+\frac{y^2}{9}=1\end{aligned}
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