Find the equation of the ellipse whose foci are (0,±6) and length of the minor axis is 16
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Solution
Since the foci of the ellipse are F1(0,−6) and F2(0,6) which lie on the y−axis and the mid-point of the line segment F1F2 is (0,0) ∴ origin is the centre of the ellipse and the major axis lies along y−axis.
Hence the equation of the ellipse can be taken as
x2b2+y2a2=1 .........(1)
Here c=6
Also, the length of the minor axis is 16
⇒2b=16
⇒b=162=8
We know that b2=a2−c2
⇒82=a2−62
⇒a2=64+36=100
From (1) , the equation of the ellipse is x264+y2100=1