Binomial Theorem

Question
CBSEENMA11015220

Find the equation of the hyperbola satisfying the given conditions.
Foci <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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#4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array)
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#6 {main}</pre> and the latus rectum is of length 8.

Solution

The foci <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)
#1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493)
#2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs()
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#4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array)
#5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array)
#6 {main}</pre> lie on the x-axis.
∴ The standard equation of the hyperbola is of the form : straight x squared over straight a squared minus straight y squared over straight b squared equals 1                 ...(i)
   The foci are      left parenthesis plus-or-minus 3 square root of 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 straight c space equals space 3 square root of 5
            The latus rectum equals 8 space rightwards double arrow space fraction numerator 2 straight b squared over denominator straight a end fraction equals 8 rightwards double arrow space straight b squared equals 4 straight a                                         ...(ii)
Now,                           straight c squared equals straight a squared plus straight b squared space rightwards double arrow space left parenthesis 3 square root of 5 right parenthesis squared space equals space straight a squared plus straight b squared space rightwards double arrow space 45 space equals space straight a squared plus 4 straight a     (∵ space space straight b squared equals 4 straight a )
rightwards double arrow             straight a squared plus 4 straight a minus 45 equals 0 space rightwards double arrow space left parenthesis straight a plus 9 right parenthesis space left parenthesis straight a minus 5 right parenthesis space equals space 0 space rightwards double arrow space straight a space equals space 5    (∵ a = -9 is not possible)
∴                       space space straight a squared equals 25
Also,                    straight c squared equals straight a squared plus straight b squared space rightwards double arrow space 45 space equals space 25 plus straight b squared space rightwards double arrow space straight b squared equals 20
Hence, from (i), the equation of the hyperbola 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)
#1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493)
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#6 {main}</pre>

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