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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