If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.

Asked by Pragya Singh | 11 months ago |  88

##### Solution :-

We know that the origin of the coordinate plane is taken at the vertex of the parabolic reflector, where the axis of the reflector is along the positive x – axis.

Diagrammatic representation is as follows

We know that 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),

y2 = 4ax

102 = 4a(5)

100 = 20a

a = $$\dfrac{100}{20}$$

= 5

The focus of the parabola is (a, 0) = (5, 0), which is the mid – point of the diameter.

Hence, the focus of the reflector is at the mid-point of the diameter.

Answered by Abhisek | 11 months ago

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