Binomial Theorem

Question
CBSEENMA11015070

Find the equation of a circle which pass through the points O (0, 0), A (4, 0) and B (0, 3).

Solution

Let the equation of the circle be <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>                       ...(i)
Since it passes through (0, 0)
∴       left parenthesis 0 minus straight h right parenthesis squared plus left parenthesis 0 minus straight k right parenthesis squared space equals space straight r squared space rightwards double arrow space straight h squared plus straight k squared equals straight r squared                                  ...(ii)
Since it passes through (4, 0)
∴        space space space space space left parenthesis 4 minus straight h right parenthesis squared plus left parenthesis 0 minus straight k right parenthesis squared equals straight r squared space rightwards double arrow space 16 plus straight h squared minus 8 straight h plus straight k squared equals straight r squared               ...(iii)
But, from (ii),          <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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#6 {main}</pre>
∴ From (iii), we have 16 minus 8 straight h plus straight r squared equals straight r squared space rightwards double arrow space 8 straight h equals 16 space rightwards double arrow space straight h equals 2
Since it passes through (0, 3)
∴      left parenthesis 0 minus straight h right parenthesis squared plus left parenthesis 3 minus straight k right parenthesis squared equals straight r squared space rightwards double arrow space straight h squared plus straight k squared minus 6 straight k plus 9 equals straight r squared rightwards double arrow straight r squared minus 6 straight k plus 9 equals straight r squared rightwards double arrow 6 straight k equals 9 rightwards double arrow straight k equals 3 divided by 2
∴ From (ii), we have
                          <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>
or              left parenthesis 4 right parenthesis plus open parentheses 9 over 4 close parentheses equals straight r squared space space or space space straight r squared equals 25 over 4 space or space straight r equals 5 over 2
Hence, the equation of circle 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>
or  space space left parenthesis straight x minus 2 right parenthesis squared plus open parentheses straight y minus 3 over 2 close parentheses squared equals 25 over 4 space or space straight x squared plus straight y squared minus 4 straight x minus 3 straight y plus 4 plus 9 over 4 equals 25 over 4
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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#6 {main}</pre>

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Some More Questions From Binomial Theorem Chapter