We know that the origin of the coordinate plane is taken at the vertex of the parabolic reflector, where the axis of the reflector is along the positive x – axis.

Diagrammatic representation is as follows

We know that the equation of the parabola is of the form y^{2} = 4ax (as it is opening to the right)

Since, the parabola passes through point A(10, 5),

y^{2} = 4ax

10^{2} = 4a(5)

100 = 20a

a = \( \dfrac{100}{20}\)

= 5

The focus of the parabola is (a, 0) = (5, 0), which is the mid – point of the diameter.

Hence, the focus of the reflector is at the mid-point of the diameter.

Answered by Abhisek | 1 year agoAn equilateral triangle is inscribed in the parabola y^{2} = 4ax, where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

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