The focus of a parabolic mirror as shown in t | vedclass

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(A) 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

Vedclass · Accepted Answer

$60$

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(A) 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 $y^{2} = 4ax$.Substituting $a = 5$,we get $y^{2} = 4(5)x = 20x$.Given that the mirror is $45 \, cm$ deep,we have $x = 45$.Substituting $x = 45$ into the equation,we get $y^{2} = 20 	imes 45 = 900$.Therefore,$y = \pm 30$.The distance $AB$ is the total length of the chord at $x = 45$,which is $2|y| = 2 	imes 30 = 60 \, cm$.

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

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