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

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- 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.

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