Binomial Theorem


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


2 straight y squared minus 9 straight x equals 0 space rightwards double arrow space straight y squared equals 9 over 2 straight x
It is equation of a parabola in the standard form straight y squared equals 4 ax comma space straight a greater than 0 and open to the right.
Comparing it with <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/ at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/ line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
#1 /home/config_admin/public/ mkdir('/home/config_ad...', 493)
#2 /home/config_admin/public/ com_wiris_util_sys_Store->mkdirs()
#3 /home/config_admin/public/ com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...')
#4 /home/config_admin/public/ com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array)
#5 /home/config_admin/public/ com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array)
#6 {main}</pre> we have space space 4 straight a equals 9 over 2 space rightwards double arrow space straight a space equals space 9 over 8

∴       Co-ordinate of focus are S (a, 0) left right arrow open parentheses 9 over 8 comma space 0 close parentheses
          Co-ordinates of vertex are (0, 0)
          Equation of axis of parabola is y = 0 (x-axis).
          Equation of tangent at the origin is x = 0 (y-axis).
          Equation of directrix is x + a = 0 or space space space straight x plus 9 over 8 equals 0 space or space 8 straight x plus 9 equals 0
      Latus rectum = 4a = 4 cross times 9 over 8 equals 9 over 2

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