Question
If a parabolic reflector is $20\ cm$ in diameter and $5\ cm$ deep, find the focus.
✓
Answer
A parabolic reflector with diameter $PR = 20\ cm$ and $OQ = 5\ cm.$
Vertex of the parabola is $(0, 0)$
Let focus of the parabola be $(a, 0).$
Now $PR = 20\ cm \Rightarrow PQ = 10\ cm$
$\therefore$ Coordinate of point P are $(5, 10)$
Since the point lies on the parabola $y^2 = 4ax$
$\therefore {(10)^2} = 4a \times 5 \Rightarrow a = \frac{{100}}{{20}} \Rightarrow a = 5$
Thus required focus of the parabola is $(5, 0).$
Vertex of the parabola is $(0, 0)$
Let focus of the parabola be $(a, 0).$
Now $PR = 20\ cm \Rightarrow PQ = 10\ cm$
$\therefore$ Coordinate of point P are $(5, 10)$
Since the point lies on the parabola $y^2 = 4ax$
$\therefore {(10)^2} = 4a \times 5 \Rightarrow a = \frac{{100}}{{20}} \Rightarrow a = 5$
Thus required focus of the parabola is $(5, 0).$
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