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Q.
The focus of a parabolic mirror as shown in figure is at a distance of $5\, cm$ from its vertex. If the mirror is $45 \,cm$ deep, find the distance $AB$.
Conic Sections
Solution:
Since the distance from the focus to the vertex is $5 \,cm$. 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, $y = ± 30$
Hence, $AB = 2y = 2 \times 30$
$= 60 \,cm$
