Binomial Theorem

Question
CBSEENMA11015168

Find the equation of the ellipse that satisfies the following condition:
Vertices (± 6, 0), foci (± 4, 0).

Solution

The foci (± 4, 0) lie on x-axis.
rightwards double arrow  Equation of ellipse in standard form is space space straight x squared over straight a squared plus straight y squared over straight b squared equals 1                        ...(i)
Foci:                       left parenthesis plus-or-minus straight c comma space 0 right parenthesis space left right arrow space left parenthesis plus-or-minus 4 comma space 0 right parenthesis space rightwards double arrow space straight c space equals space 4
Vertices:               space space left parenthesis plus-or-minus straight a comma space 0 right parenthesis space left right arrow space left parenthesis plus-or-minus 6 comma space 0 right parenthesis space rightwards double arrow space straight a equals 6 space or space straight a squared equals 36
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#6 {main}</pre>
∴  From (i), equation of ellipse is straight x squared over 36 plus straight y squared over 20 equals 1

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