Question

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

• A. (2,0)
• B. (3,0)
• C. (4,0)
• D. (5,0)

Answer 1

Answer: (D)

Taking vertex of the parabolic reflector at origin, x-axis along the axis of parabola. The equation of the parabola is $y^2=4ax$. Given depth is $5cm$, diameter is $20cm$
$\because$ Point $P(5,10)$ lies on parabola.
$\therefore (10{)}^2=4a(5)$
$\Rightarrow a=5$
Clearly, focus is at the mid-point of given diameter.

i.e., $S=(5,0)$