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Q.
If a parabolic reflector is $20 cm$ in diameter and $5 cm$ deep, then the focus is
Conic Sections
Solution:
Taking vertex of the parabolic reflector at origin, $X$-axis along the axis of parabola. The equation of the parabola is $y^2=4 a x$.
Given depth is $5 cm$, diameter is $20 cm$.
$\because$ Point $P(5,10)$ lies on parabola.
$\therefore (10)^2=4 a(5) \rightarrow a=5$
Clearly, focus is at the mid-point of given diameter.
