Binomial Theorem

Question
CBSEENMA11015129

Find the equation of a parabola that satisfies the given condition:
Focus (0 – 3); directrix y = 3

Solution

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 straight x squared equals negative 4 ay                 ...(i)
Focus is (0, -a) left right arrow (0, -3) and directrix y - a = 0 is y - 3 = 0   rightwards double arrow  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 straight P space left parenthesis straight alpha comma space straight beta right parenthesis on the parabola. From P, draw PM perpendicular on the directrix l and join PS. By definition of parabola, PS = PM
rightwards double arrow           square root of left parenthesis straight alpha minus 0 right parenthesis squared plus left parenthesis straight beta plus 3 right parenthesis squared end root space equals space open vertical bar fraction numerator straight beta minus 3 over denominator 0 squared plus left parenthesis 1 right parenthesis squared end fraction close vertical bar
rightwards double arrow            square root of straight alpha squared plus straight beta squared plus 6 straight beta plus 9 end root space equals space open vertical bar straight beta minus 3 close vertical bar
rightwards double arrow            straight alpha squared plus straight beta squared plus 6 straight beta plus 9 space equals space straight beta squared plus 9 minus 6 straight beta space rightwards double arrow space straight alpha squared plus 12 straight beta space equals space 0
Hence, the equation of locus of P i.e, equation of parabola is straight x squared plus 12 straight y equals 0
                                              

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