Multiple Choice Questions

What is the distance between the foci of the ellipse x2 2y2 1 ........

Mathematics (NDA) Coordinate Geometry

What is the distance between the foci of the ellipse x² + 2y² = 1 ?

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2022 NDA -1 Math

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2√2

- The given equation is $\frac{x^{2}}{1} + \frac{y^{2}}{\frac{1}{2}} = 1$ .

- This is the equation of an ellipse in the form $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ .

- Here, $a^{2} = 1$ and $b^{2} = \frac{1}{2}$ .

- The foci distance for an ellipse is found using $c^{2} = a^{2} - b^{2}$ .

- Calculate $c$ :

- $c^{2} = 1 - \frac{1}{2} = \frac{1}{2}$ .

- Therefore, $c = \sqrt{\frac{1}{2}} = \frac{\sqrt{2}}{2}$ .

- Distance between the foci is $2 c = 2 \times \frac{\sqrt{2}}{2} = \sqrt{2}$ .

- Answer: Option 2 ( $\sqrt{2}$ )

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