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Binomial Theorem

Question
CBSEENMA11015169
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Find the equation of the ellipse that satisfies the following condition:
Vertices (0, ± 13), foci (0, ± 5).

Solution

The foci (0, ± 5) lie on y-axis.
∴ Equation of ellipse in standard form is space space straight y squared over straight a squared plus straight x squared over straight b squared equals 1                                     ...(i)
Foci:                     left parenthesis 0 comma space plus-or-minus 5 right parenthesis space left right arrow space left parenthesis 0 comma space plus-or-minus straight c right parenthesis space space rightwards double arrow space space straight c space equals space 5
Vertices:              space space left parenthesis 0 comma space plus-or-minus straight a right parenthesis space left right arrow space left parenthesis 0 comma space plus-or-minus 13 right parenthesis space rightwards double arrow space straight a space equals space 13               rightwards double arrow WiredFaculty
Now,                             straight c squared equals straight a squared minus straight b squared space space space space space space rightwards double arrow space space 25 space equals space 169 minus straight b squared space space space rightwards double arrow space space straight b squared equals 144
Hence, from (i), the equation of the ellipse is straight y squared over 169 plus straight x squared over 144 equals 1

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