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.
$\therefore (10{)}^2=4a(5)\to a=5$
Clearly, focus is at the mid-point of given diameter.