Question

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

• A. $(0,5)$
• B. $(0,0)$
• C. $(5,0)$
• D. $(5,5)$

Answer 1

The correct option is C $(5,0)$

Taking vertex of the parabola reflector of origin, x-axis along the axis of the parabola the equation of a parabola is $y^2=4ax$. Given depth $5cm$ diameter $20cm$

$\therefore (5,10)$ point lies on a parabola.

$\therefore a=5$

$\therefore$ Focus is $(a,0)$, i.e. $(5,0)$ which is mid-point of the given diameter