Binomial Theorem

Question
CBSEENMA11015172

Find the equation of an ellipse that satisfy the following condition:
Length of major axis 26, foci (± 5, 0).

Solution

The foci (± 5, 0) are on x-axis.
∴  The 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 are               left parenthesis plus-or-minus 5 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 space straight c space equals space 5
   Length of major axis 2a = 26 rightwards double arrow   a = 13 or  <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
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Also,                      straight c squared equals straight a squared minus straight b squared space rightwards double arrow space 5 squared equals 13 squared minus straight b squared space rightwards double arrow space 25 space equals space 169 minus straight b squared space rightwards double arrow space straight b squared equals 169 minus 25 space equals space 144
∴ From (i), equation of ellipse is : straight x squared over 169 plus straight y squared over 144 equals 1
Let e be the eccentricity
∴                       c = ae  rightwards double arrow 5 = 13e rightwards double arrow  straight e equals 15 over 13

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