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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, then the distance $A B$ is
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
$y^2=4(5) x=20 x$
Note that $x=45$. Thus, $y^2=900$
Therefore, $ y=\pm 30$
Hence, $ A B=2 y=2 \times 30=60 cm$.
