Binomial Theorem

Question
CBSEENMA11015087

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?

Solution

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: <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>
Comparing it with the standard form of circle <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>, 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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