Binomial Theorem


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


straight x squared space equals negative 9 straight y space or space straight x squared plus 9 straight y equals 0
It is equation of parabola in the standard form space space space space straight x squared equals negative 4 ay comma space straight a greater than 0 and it open towards.
Comparing the equation 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 negative 4 straight a space equals negative 9 space or space straight a equals 9 over 4

∴ (i) the focus is S(0, -a) left right arrow open parentheses 0 comma space fraction numerator negative 9 over denominator 4 end fraction close parentheses
   (ii) the equation of axis is x = 0 (y-axis).
   (iii) the equation of tangent at the origin is y = 0 (x-axis)
   (iv) the equation of directrix is y - a = 0 or straight y minus 9 over 4 space equals space 0 space or space 4 straight y minus 9 space equals 0
   (v) the length of the latus rectum = 4a = 4 cross times 9 over 4 equals 9

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