Binomial Theorem


Find the area of the triangle formed by the lines joining the vertex of the parabola x2 = 12y to the ends of the latus rectum. 


The equation of the parabola is straight x squared equals 12 straight y.
rightwards double arrow                    4a = 12   or   a = 3
Focus S is (0, a) left right arrow (0, 3)
rightwards double arrow                 OS = 3
                      LL' = length of the latus rectum
                           = 4a = 12
Hence, area of ΔOLL apostrophe space equals space 1 half left parenthesis LL apostrophe right parenthesis space cross times space OS
                                 equals 1 half cross times 12 cross times 3 space equals space 18 space square space units.

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