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Conic Section

Short Answer Type

1. In each of the following, find the equation of circle with centre (-2, 3) and radius 4

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2. In each of the following, find the equation of circle with centre

open parentheses 1 half comma space 1 fourth close parentheses

and radius

1 over 12

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3. In each of the following, find the equation of circle with centre (-a, -b) and radius

space space space space square root of straight a squared minus straight b squared end root

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4. Find the equation of a circle with centre at (2, 2) and passes through the point (4,5).

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Long Answer Type

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

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6. Find the equation of the circle passes through (0, 0) and making intercepts a and b on the co-ordinate axes.

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Short Answer Type

7. Find the equation of a circle whose centre is (3, –2) and has an area of 154 square units.

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8. Find the equation of a circle having radius 5 units and the centre as the point of intersection of the straight lines 2x – y – 5 = 0 and 3x + 2y = 4.

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9. Find the equation of a circle, two of whose diameters are along the straight lines x – 2y = 7 and x + 2y + 1 = 0 and which passes through the point (1, 4).

Let AB and EF be the two diameters of the circle and have equations
x - 2y = 7 and x + 2y = -1 respectively.
The centre C of the circle is the point of intersection of the two diameters
∴ For C,
x - 2y = 7 ...(i)
x + 2y = -1 ...(ii)
Adding, we get 2x = 6 $rightwards double arrow$ x = 3
and 3 - 2y = 7 $rightwards double arrow$ y = -2
∴ The co-ordinates of centre C of the circle are (3, -2)
Also, the circle passes through point P(1, 4)
∴ Radius of the circle, r = CP = $space space square root of left parenthesis 1 minus 3 right parenthesis squared plus left parenthesis 4 plus 2 right parenthesis squared end root equals space square root of 4 plus 36 end root space equals space square root of 40$
$rightwards double arrow$ h = 3, k = -2, $space space straight r equals square root of 40$
The equation of the circle is:
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or $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$
which is the required equation of the circle.

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10. Find the equation of a circle having centre at point C(–2, 3) and touching the straight line 3x – 4y – 2 = 0.

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