The equation of the ellipse having foci (0, 1), (0, â€“1), and a minor axis of length 1 is ______.

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Alok Kumar Singh | Contributor-Level 10

a year ago

This is a Fill in the Blanks Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l} W e k n o w t h a t t h e f o c i o f t h e e l l i p s e a r e (0, \pm a e) a n d g i v e n f o c i a r e (0, \pm 1), s o a e = 1 \\ L e n g t h o f minor a x i s = 2 b = 1 \Rightarrow b = \frac{1}{2} \\ W e k n o w t h a t b^{2} = a^{2} (1 - e^{2}) \\ {(\frac{1}{2})}^{2} = a^{2} - a^{2} e^{2} \\ \Rightarrow \frac{1}{4} = a^{2} - 1 \Rightarrow a^{2} = 1 + \frac{1}{4} = \frac{5}{4} \\ ∴ E q u a t i o n o f a n e l l i p s e i s \frac{x^{2}}{b^{2}} + \frac{y^{2}}{a^{2}} = 1 \\ \Rightarrow \frac{x^{2}}{1 / 4} + \frac{y^{2}}{5 / 4} = 1 \\ \Rightarrow \frac{4 x^{2}}{1} + \frac{4 y^{2}}{5} = 1 \\ H e n c e, t h e v a l u e o f f i l l e r i s \frac{4 x^{2}}{1} + \frac{4 y^{2}}{5} = 1 . \end{array}$

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Start with

(1) $\bar{E} : \frac{6!}{2!} = 360$

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