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Question

The equation of the ellipse having foci (0, 1),(0, –1) and minor axis of length 1 is ___________.

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Solution

For an ellipse, length of minor axis is given = l and foci is given by = (0, ±1)
i.e ellipse is of the form x2a2+y2b2=1 ; a<b
i.e be = ±1
Also, 2a = 1 i.e 1a= 2
i.e a = 12
and e = ±1b
Since eccentricity e=1-a2b2 i.e e2=1-a2b2i.e 1b2=1-14b2 1b2+14b2=1 i.e 4+14b2=1 i.e 1b2=45 x2a2+y2b2=1i.e x214+4y25=1i.e 4x2+4y25=1i.e 20x2+4y2 =5

Hence, equation of ellipse is 20x2 + 4y2 = 5.

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