Binomial Theorem


Find the equation of the parabola that satisfying the following condition:
Vertex at (0,0), focus on the positive x-axis and length of latus rectum 16 over 9.


The vertex is (0, 0) and the focus on positive x-axis is S (a, 0), a>0
∴  Equation of parabola is straight y squared equals 4 ax                                                      ...(i)
Latus rectum = 4a = 16 over 9                                                         (∵ a > 0)
Hence, from (i), the equation of parabola is: straight y squared equals 16 over 9 straight x space or space 9 straight y squared equals 16 straight x

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