if the parabolic reflector is 20cm in diameter and 5cm 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. This can be diagrammatically represented as;
The equation of the parabola is of the form y2 = 4ax (as it is opening to the right).
Since the parabola passes through point A (10, 5), 102 = 4a(5)
⇒ 100 = 20a
⇒ a =100/20 =5
Therefore, the focus of the parabola is (a, 0) = (5, 0), which is the midpoint of the diameter.
Hence, the focus of the reflector is at the midpoint of the diameter.
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. This can be diagrammatically represented as;
The equation of the parabola is of the form y2 = 4ax (as it is opening to the right).
Since the parabola passes through point A (10, 5), 102 = 4a(5)
⇒ 100 = 20a
⇒ a =100/20 =5
Therefore, the focus of the parabola is (a, 0) = (5, 0), which is the midpoint of the diameter.
Hence, the focus of the reflector is at the midpoint of the diameter.
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