Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

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

79 Views

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

100 Views

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

98 Views

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.
$4 straight x squared plus 9 straight y equals 0$

4 straight x squared plus 9 straight y equals 0 space space rightwards double arrow space straight x squared space equals space minus 9 over 4 straight y

It is equation of a parabola in the standard form

space straight x squared equals negative 4 ay comma space straight a greater than 0

and open towards
Comparing with

straight x squared equals negative 4 ay comma space we space have space minus 4 straight a space equals space minus 9 over 4 space rightwards double arrow space straight a equals 9 over 16

Co-ordinates of focus are (0, -a) =

open parentheses 0 comma space fraction numerator negative 9 over denominator 16 end fraction close parentheses

Co-ordinates of vertex are (0, 0)

Equation of axis is x = 0 (y-axis)
Equation of tangent at origin is y = 0 (x-axis)
Equation of directrix is y - a = 0 or

<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>

Length of latus -rectum = 4a =

4 cross times 9 over 16 equals 9 over 4

87 Views

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

429 Views

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

104 Views

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

83 Views

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

92 Views

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.

80 Views

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)

87 Views