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19. Find the centre and radii of the following circle:
$space space 2 straight x squared plus 2 straight y squared minus straight x equals 0$

The given equation of the circle is: $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ (Note this step)
$rightwards double arrow$ $open parentheses straight x squared minus straight x over 2 close parentheses plus straight y squared space equals space 0 space rightwards double arrow space open square brackets straight x squared minus straight x over 2 plus open parentheses 1 fourth close parentheses squared close square brackets plus straight y squared equals 0 plus open parentheses 1 fourth close parentheses squared space rightwards double arrow space open parentheses straight x minus 1 fourth close parentheses squared plus left parenthesis straight y minus 0 right parenthesis squared space equals space open parentheses 1 fourth close parentheses squared$
Comparing it with the standard equation of the circle, $left parenthesis straight x minus straight h right parenthesis squared plus left parenthesis straight y minus straight k right parenthesis squared equals straight r squared comma$ we have
$space space space straight h equals 1 fourth comma space space straight k equals 0 space space and space straight r equals 1 fourth$
∴ the centre of the circle is $left parenthesis straight h comma space straight k right parenthesis space left right arrow space open parentheses 1 fourth comma space 0 close parentheses space radius space is space 1 fourth$