Binomial Theorem

Question
CBSEENMA11015163

In the following, find the co-ordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
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Solution

Equation of ellipse is <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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                            space space space space 100 greater than 25 space rightwards double arrow space space space straight a squared equals 100 comma space straight b squared equals 25
∴ Equation of ellipse in the standard form is space space straight y squared over straight a squared plus straight x squared over straight b squared equals 1
Co-ordinates of foci
Focus,    straight S subscript 1 left right arrow left parenthesis 0 comma space minus straight c right parenthesis space left right arrow space left parenthesis 0 comma space minus square root of straight a squared minus straight b squared end root right parenthesis space left right arrow space left parenthesis 0 comma space minus square root of 100 minus 25 end root right parenthesis space left right arrow space left parenthesis 0 comma space minus square root of 75 right parenthesis space left right arrow space left parenthesis 0 comma space minus 5 square root of 3 right parenthesis
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Co-ordinates of vertices
Vertex, straight A space left right arrow space left parenthesis 0 comma space straight a right parenthesis space left right arrow space left parenthesis 0 comma space 10 right parenthesis
Vertex,                              <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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Length of major axis = 2a = 2 x 10 = 20
Length of minor axis = 2b = 2 x 5 = 10
Let e be the eccentricity. Now, c = ae rightwards double arrow 5 square root of 3 space equals space 10 straight e space rightwards double arrow space straight e space equals space fraction numerator 5 square root of 3 over denominator 10 end fraction
∴                         straight e equals fraction numerator square root of 3 over denominator 2 end fraction
Latus rectum,  l equals fraction numerator 2 straight b squared over denominator straight a end fraction equals fraction numerator 2 cross times 25 over denominator 10 end fraction equals 5

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