If a parabolic reflector is 20 , cm in diamet | vedclass

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(A) The origin of the coordinate plane is taken at the vertex of the parabolic reflector such that the axis of the reflector is along the positive $x-

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$(5, 0)$

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(A) The origin of the coordinate plane is taken at the vertex of the parabolic reflector such that the axis of the reflector is along the positive $x-$axis.The equation of the parabola is of the form $y^{2} = 4ax$ (as it opens to the right).The depth of the reflector is $5 \, cm$,so the $x-$coordinate of the point on the rim is $5$. The diameter is $20 \, cm$,so the $y-$coordinate of the point on the rim is $10$ (half of the diameter).Thus,the parabola passes through the point $A(5, 10)$.Substituting this into the equation $y^{2} = 4ax$:$10^{2} = 4a(5)$$100 = 20a$$a = \frac{100}{20} = 5$Therefore,the focus of the parabola is $(a, 0) = (5, 0)$.

If a parabolic reflector is $20 \, cm$ in diameter and $5 \, cm$ deep,find the focus.

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