If a parabola reflector with its axis as x−axis is 20 cm in diameter and 5 cm deep. Find the focus.
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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 x-axis. The equation of the parabola is of the form y2=4ax (as it is opening to the right)
Given, diameter of parabola =20 cm
Since, parabola is symmetric about x-axis.
So, co-ordinates of point A are (5,10) Since the parabola passes through the point A(5,10)
102=4a(5) ⇒100=20a ⇒a=20100=5 Therefore, the focus of the parabola is (a,0)=(5,0) which is the mid-point of the diameter.