Binomial Theorem

Question
CBSEENMA11015212

Find the co-ordinates of foci, the vertices, the lenghts of transverse and conjugate axis, the eccentricity the length of latus rectum of hyperbola
16 straight x squared minus 9 straight y squared equals 576

Solution

The equation of hyperbola is : 16 straight x squared minus 9 straight y squared equals 576
rightwards double arrow             <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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#6 {main}</pre> which is of the form straight x squared over straight a squared minus straight y squared over straight b squared equals 1
∴ The foci and vertices lie on x-axis.
So,                                       <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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#6 {main}</pre>
                                            straight b squared equals 64 space rightwards double arrow space straight b equals 8
∴                                        space space straight c squared equals straight a squared plus straight b squared space rightwards double arrow space straight c squared equals 36 plus 64 equals 100 space rightwards double arrow space straight c space equals space 10
The co-ordinates of foci are:
                          straight S subscript 1 left parenthesis negative straight c comma space 0 right parenthesis space left right arrow space left parenthesis negative 10 comma space 0 right parenthesis
space space straight S subscript 2 left parenthesis straight c comma space 0 right parenthesis space left right arrow space left parenthesis 10 comma space 0 right parenthesis
The co-ordinates of the vertices are:
                            straight A left parenthesis straight a comma space 0 right parenthesis space left right arrow space left parenthesis 6 comma space 0 right parenthesis
                        straight A apostrophe left parenthesis negative straight a comma space 0 right parenthesis space left right arrow space left parenthesis negative 6 comma space 0 right parenthesis
The length of transverse axis = 2a = 2 x 6 = 12
The length of conjugate axis = 2b = 2 x 8 = 16
Let the eccentricity be e, we know that c = ae rightwards double arrow 10 = 6e rightwards double arrow straight e equals 10 over 6 equals 5 over 3
The length of latus rectum <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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#6 {main}</pre>
                             

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