Binomial Theorem

Question
CBSEENMA11015176

Find the equation of an ellipse for which foci are at (± 3, 0), a = 4 and centre is at origin. Also, find the eccentricity of the ellipse.

Solution

The foci left parenthesis plus-or-minus 3 comma space 0 right parenthesis lie on x-axis.
∴ The equation of ellipse in standard form is straight x squared over straight a squared plus straight b squared over straight b squared equals 1
Foci left parenthesis plus-or-minus 3 comma space 0 right parenthesis space left right arrow space left parenthesis plus-or-minus straight c comma space 0 right parenthesis space rightwards double arrow space straight c space equals space 3
Also,         a = 4 (given)
Using,        straight c squared equals straight a squared minus straight b squared comma space we space get space 9 space equals space 16 minus straight b squared space rightwards double arrow space straight b squared equals 7
Hence, from (i), the equation of ellipse is : straight x squared over 16 plus straight y squared over 7 equals 1
Also,                       c = ae rightwards double arrow   3 = 4e rightwards double arrow  straight e equals 3 over 4

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