Derive the analytic equation of a parabola with focus (0,10) and directrix on the x-axis.

  y= (ײ/20) + 10

Step-by-step explanation:

The general equation for parabola is of the form:

   (x -h)² = + 4p (y-k)

Where the vertex is the point (h,k) and p is the distance between the vertex and the directrix, therefore

Focus of parabola is the point (0,10) and the directrix on the x-axis

so the vertex of parabola is the point (0,5) and p = 5

Hence

(× - 0)² = 4*5 (y-10)   ⇒   x² = 20y -200  ⇒ x² +200 = 20y   ⇒  y= (ײ/20) + 10

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