Question

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

Answer 1

The diameter of the parabolic reflector is 20 cm and the depth is 5 cm.

Let the origin of the coordinate plane be at the vertex of the parabolic reflector in such a way that the axis of reflector is along the x axis.

Assume that the parabola opens to the right.

The equation of the parabola along with x axis and opening towards right is,

y 2 =4ax

The parabola passes through the point A( 5,10 ). So,

10 2 =4×a×5 100 20 =a a=5

Thus, the focus of the parabolic reflector with diameter 20 cmand the depth 5 cm is ( 5,0 ).