Binomial Theorem

Question
CBSEENMA11015128

Find the equation of a parabola that satisfies the given condition:
Focus (6, 0), directrix is x = – 6

Solution

The focus is S(6, 0) which lies on x-axis.
The directrix is x + 6 = 0 which is a line parallel to y-axis i.e., perpendicular to x-axis.
∴   The parabola is of the standard form straight y squared equals 4 ax.
Also, focus (a, 0) left right arrow (6, 0) directrix x + a = 0 is x + 6 = 0 rightwards double arrow a = 6
Hence, the equation of the parabola is straight y squared equals 4 space left parenthesis 6 right parenthesis space straight x space or space straight y squared equals 24 straight x
Alternative method:
Let line be the directrix with equation x + 6 = 0
The focus is S (6, 0). Take a point straight P space left parenthesis straight alpha comma space straight beta right parenthesis on the parabola.
From P, draw PM perpendicular on directrix l and join PS. By definition of parabola, PS = PM
rightwards double arrow                                      d = p
rightwards double arrow      square root of left parenthesis straight alpha minus 6 right parenthesis squared plus left parenthesis straight beta minus 0 right parenthesis squared end root space equals space open vertical bar fraction numerator straight alpha plus 6 over denominator square root of left parenthesis 1 right parenthesis squared plus 0 squared end root end fraction close vertical bar
                                           equals square root of left parenthesis straight alpha minus 6 right parenthesis squared plus straight beta squared end root space equals space open vertical bar straight a plus 6 close vertical bar
Squaring both sides, we get
space space space space space space straight alpha squared minus 12 straight alpha plus 36 plus straight beta squared space equals space straight alpha squared plus 12 straight alpha plus 36 space rightwards double arrow space straight beta squared minus 24 straight alpha space equals space 0
Hence, the locus of P i.e., the equation of parabola 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)
#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()
#3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...')
#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>
                                            

Sponsor Area

Some More Questions From Binomial Theorem Chapter