Question

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

Answer 1

Let equation of parabola be

$y^2=4ax.......\left(1\right)$

Parabola is 5 cm deep

Hence, $OC=5cm$

So, x-coordinate of point A=5

It can be seen from figure

$AB=20cm$

Since parabola is symmetric along x-axis

$AC=\frac{1}{2}\times AB=10cm$

Hence coordinates of point A is (5,10)

Since point A (5,10) lies on the parabola, it will satisfy the equation of the parabola.

Putting x=5 and y=10 in (1), we get

$y^2=4ax$

${10}^2=4\times a\times 5$

$100=20a$

$a=5$

Thus, Focus is $(a,0)=(5,0)$