Short Answer Type
The focus of parabola is (0, -3) which lies on y-axis. Directrix of the parabola is y - 3 = 0 which is parallel to x-axis.
∴ The equation of the parabola is of the standard form 
...(i)
Focus is (0, -a) 
(0, -3) and directrix y - a = 0 is y - 3 = 0 
a = 3
Hence, form (i), the equation of the parabola is ![<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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Alternative method:
Let l be the directrix with equation y - 3 = 0.
S (0, -3) is the focus.
Take a point 
on the parabola. From P, draw PM perpendicular on the directrix l and join PS. By definition of parabola, PS = PM
Hence, the equation of locus of P i.e, equation of parabola is 
An equilateral triangle is inscribed in the parabola 
, where one vertex is at the vertex of the parabola. Find (a) the length of the side of the triangle, (b) area of triangle ABC.
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