Binomial Theorem

Question
CBSEENMA11015119

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


Solution

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)
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      Length of latus -rectum = 4a = 4 cross times 9 over 16 equals 9 over 4
        

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