Question

If a parabola reflector with its axis as is cm in diameter and cm deep. Find the focus.

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Solution

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The origin of the coordinate plane is taken at the vertex of the parabolic reflector in such a way that the axis of the reflector is along the positive -axis.
The equation of the parabola is of the form  (as it is opening to the right)
Given, diameter of parabola cm
Since, parabola is symmetric about -axis.
So, co-ordinates of point are
Since the parabola passes through the point 



Therefore, the focus of the parabola is which is the mid-point of the diameter.

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