Q176 / 270 · NDA 2010 (Phase 1) · Mathematics

If $(4,0)$ and $(-4,0)$ are the foci of an ellipse and the semi-minor axis is 3 ; then the ellipse passes through which one of the following points?

  • A
    $(2,0)$
  • B
    $(0,5)$
  • C
    $(0,0)$
  • Correct answer
    D
    $(5,0)$

Solution

$\begin{aligned} & \text { Focus }=( \pm a e, o) \\ & b=3, \text { and } \\ & 2 b=6 \\ & a e=4 \\ & \text { But } c=4 \\ & \therefore c=\sqrt{a^2-b^2} \\ & \Rightarrow 1 b=a^2-b^2 \text { or } a^2=16+9 \\ & \therefore a=5, b=3 \\ & \therefore \frac{x^2}{25}+\frac{b^2}{9}=1 \end{aligned}$ which clearly passes through $(5,0)$

Hence, the correct answer is option: 'D'.

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