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Conic Section

Short Answer Type

51. In the following, find the co-ordinates of the focus, axis of the parabola, the equation of the directrix and length of the latus rectum.

space space space space straight x squared equals 6 straight y

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52. In the following, find the co-ordinates of the focus, axis of the parabola, the equation of the directrix and length of the latus rectum.

straight x squared space equals negative 9 straight y

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53. Find: the co-ordinates of the focus and the vertex, the equations of axis, tangent at the vertex and directrix, the length of latus rectum of the parabola.

2 straight y squared minus 9 straight x equals 0

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54. Find: the co-ordinates of the focus and the vertex, the equations of axis, tangent at the vertex and directrix, the length of latus rectum of the parabola.

4 straight x squared plus 9 straight y equals 0

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55. Find the equation of the parabola whose focus is at point S (2, 5) and the directrix is line 3x + 4y + 1 = 0.

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56. Find the equation of the parabola whose vertex is at (0, 0) and the focus is at point S (5, 0).

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57. Find the equation of the parabola whose vertex is at (0, 0) and the focus is at point (-3, 0).

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58. Find the equation of the parabola whose vertex is at (0, 0) and focus is at (0, – 2).

The vertex of the parabola is at O(0, 0) and the focus at S (0, -2). For both the points, x = 0.
$rightwards double arrow$ The x-axis of the parabola is along x = 0 or the y-axis.
$rightwards double arrow$ The equation of the parabola in the standard form is $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ ...(i)
Also, the focus $straight S space left parenthesis 0 comma space straight a right parenthesis space left right arrow space left parenthesis 0 comma space minus 2 right parenthesis space rightwards double arrow space straight a space equals space minus 2$
Hence, the equation of the parabola is: $straight x squared equals 4 left parenthesis negative 2 right parenthesis space straight y space or space straight x squared equals negative 8 straight y$

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59. Find the equation of the parabola that satisfying the following condition:
Vertex (0,0) passing through (2,3) and axis is along x-axis.

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60. Find the equation of the parabola that satisfying the following condition:
Vertex at (0,0), symmetrical about y-axis and passing through the point (2, –3)

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