The equation is y^{2} = 12x

Here we know that the coefficient of x is positive.

So, the parabola opens towards the right.

On comparing this equation with y^{2} = 4ax, we get,

4a = 12

a = 3

Thus, the co-ordinates of the focus = (a, 0) = (3, 0)

Since, the given equation involves y^{2}, the axis of the parabola is the x-axis.

The equation of directrix, x = -a, then,

x + 3 = 0

Length of latus rectum = 4a

= 4 × 3 = 12

Answered by Abhisek | 11 months 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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