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प्रश्न
The equation of the ellipse having foci (0, 1), (0, –1) and minor axis of length 1 is ______.
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उत्तर
The equation of the ellipse having foci (0, 1), (0, –1) and minor axis of length 1 is `bbunderline((4x^2)/1 + (4y^2)/5 = 1)`.
Explanation:
We know that the foci of the ellipse are (0, ± ae)
And given foci are (0, ± 1)
So be = 1
Length of minor axis = 2b = 1
⇒ `b = 1/2`
We know that b2 = a2 (1 – e2)
⇒ `1/4 = a^2 - 1`
⇒ `a^1 = 1 + 1/4 = 5/4`
∴ Equation of ellipse is `x^2/b^2 + y^2/a^2` = 1
⇒ `x^2/(1/4) + y^2/(5/4)` = 1
⇒ `(4x^2)/1 + (4y^2)/5` = 1
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