8. An equilateral triangle is inscribed in the parabola , where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.
Given, an equilateral triangle inscribed in parabola with the equation.
The one coordinate of the triangle is A(0,0).
Now, let the other two coordinates of the triangle are
Now, Since the triangle is equilateral,
The coordinates of the points of the equilateral triangle are,
So, the side of the triangle is