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Conic Section

Long Answer Type

101.

Find: (i) the co-ordinates of foci.
(ii) the co-ordinates of vertices.
(iii) the length of major axis and minor axis.
(iv) the eccentricity.
(v) latus rectum of ellipse.
$4 straight x squared plus 9 straight y squared equals 1$

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102.

Find: (i) the co-ordinates of foci.
(ii) the co-ordinates of vertices.
(iii) the length of major axis and minor axis.
(iv) the eccentricity.
(v) latus rectum of ellipse.
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Short Answer Type

103. Find the equation of the ellipse that satisfies the following condition:
Vertices (± 6, 0), foci (± 4, 0).

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104. Find the equation of the ellipse that satisfies the following condition:
Vertices (0, ± 13), foci (0, ± 5).

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105. Find the equation of an ellipse that satisfies the following conditions
Ends of major axis at

<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() #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>

, ends of minor axis at

left parenthesis 0 comma space plus-or-minus 2 right parenthesis

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106. Find the equation of an ellipse that satisfies the following conditions
Ends of major axis at

space left parenthesis 0 comma space plus-or-minus square root of 13 right parenthesis comma

ends of minor axis at

space space left parenthesis plus-or-minus 2 comma space 0 right parenthesis

. Also find the co-ordinate of foci.

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107. Find the equation of an ellipse that satisfy the following condition:
Length of major axis 26, foci (± 5, 0).

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108. Find the equation of an ellipse that satisfy the following condition:
Length of minor axis 16, foci (0, ± 6). Find also, the eccentricity .

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109. Find the equation of an ellipse whose major axis is along the x-axis and which passes through the points (6, 3) and (12, 0).

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110. Find the equation of an ellipse whose major axis is along the y-axis and which passes through the points P (2, 2) and Q (1, 4).

The major axis is along the y-axis.
∴ The equation of ellipse in the standard form is $space space straight y squared over straight a squared plus straight x squared over straight b squared equals 1$ ...(i)
It passes through (2, 2) $rightwards double arrow$ $space space 4 over straight a squared plus 4 over straight b squared equals 1$ ...(ii)
It passes through (1, 4) $rightwards double arrow$ $16 over straight a squared plus 1 over straight b squared equals 1$ ...(iii)
Multiplying both sides of (ii) by 4, we get
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Subtracting (iv) from (iii), we get $fraction numerator negative 15 over denominator straight b squared end fraction equals negative 3 space space rightwards double arrow space space straight b squared equals 5$
∴ From (iii), $16 over straight a squared plus 1 fifth equals 1 space space rightwards double arrow space space 16 over straight a squared equals 1 minus 1 fifth equals 4 over 5 space rightwards double arrow space straight a squared equals 16 cross times 5 over 4 equals 20$
Hence, from (i), the equation of ellipse is: $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

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