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Conic Section

Short Answer Type

21.

Does the point (-2.5, 3.5) lie inside, outside or on the circle $straight x squared plus straight y squared equals 25$ ?

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22.
Does the point (2, -1) lie inside, or on the circle $straight x squared plus straight y squared plus 6 straight x minus 2 straight y minus 6 equals 0$ ?

The equation of the circle is: $straight x squared plus straight y squared plus 6 straight x minus 2 straight y minus 6 equals 0$
$rightwards double arrow$ $left parenthesis straight x squared plus 6 straight x right parenthesis plus left parenthesis straight y squared minus 2 straight y right parenthesis space equals space 6 space rightwards double arrow space left parenthesis straight x squared plus 6 straight x plus 9 right parenthesis plus left parenthesis straight y squared minus 2 straight y plus 1 right parenthesis space equals space 6 plus 9 plus 1$
$rightwards double arrow$ $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$
Comparing it with the standard form of circle $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ , we have
$straight h equals negative 3 comma space straight k equals 1 space and space straight r space equals space 4$

∴ The centre is C (-3, 1) and radius is r = 4
Distance of point A (2, -1) from the centre.
$CA space equals space square root of left parenthesis negative 3 minus 2 right parenthesis squared plus left parenthesis 1 plus 1 right parenthesis squared end root space equals space square root of 25 plus 4 end root space equals space square root of 29 greater than 4$
∴ Distance of point from the centre is greater than the radius.
Hence, the point lies outside the circle.

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23.

Find the equation of the circle whose centre and radii are:
Centre (-3, -2), radius 7

91 Views

24.

Find the equation of the circle whose centre and radii are:
Centre (a, a), radius $space square root of 2 straight a$

104 Views

25.

Find the equation of the circle whose centre and radii are:
Centre $open parentheses 1 half comma space 1 half close parentheses comma space radius space fraction numerator 1 over denominator square root of 2 end fraction$