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

$\begin {array} {1 1} (A)\;a=-5 & \quad (B)\;a=5 \\ (C)\;a=10 & \quad (D)\;a=-10 \end {array}$

Toolbox:
• Standard equation of a parabola which is open rightward is $y^2=4ax$ where a is the focus.
Step 1 :
Let the origin be the vertex of the parabola and axis is along x - axis.
Since the parabola is open rightward
The equation of the parabola is $y^2=4ax$
Step 2 :
Since the parabola passes through the point $A(10, 5)$, substituting the values for x and y we get,
$(10)^2=4 \times a \times 5$
$\Rightarrow 100 = 20a$
$\therefore a = 5$
Hence the focus of the reflector is 5, which is the midpoint of the diameter.