Question

The focus of a parabolic mirror as shown in figure is at a distance of $5cm$ from its vertex. If the mirror is $45cm$ deep, find the distance $AB$.

• A. $30cm$
• B. $45cm$
• C. $60cm$
• D. $90cm$

Answer 1

Answer: (C)

Since the distance from the focus to the vertex is $5cm$. We have, $a=5$. If the origin is taken at the vertex and the axis of the mirror lies along the positive $x$-axis, the equation of the parabolic section is

$y^2=4(5)x=20x$
We have, $x=45$,
so $y^2=900$
Therefore, $y=\pm 30$
Hence, $AB=2y=2\times 30$
$=60cm$