NCERT Class 11 Mathematics Solutions: Chapter 11 –Conic Sections Miscellaneous Exercise 11 Part 5

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In figure equation of parabola is shown.

Equation of Parabola

In figure equation of parabola is shown.

1. 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.

Answer:

Consider be the equilateral triangle inscribed in parabola .

Consider intersect the x-axis at point .

The Equilateral Triangle Inscribed in Parabola

The equilateral triangle inscribed in parabola AB intersect the x-axis at point C

Consider

From the equation of the given parabola

We have,

The respective coordinates of points are

So, is an equilateral triangle,

So, the side of the equilateral triangle inscribed in parabola is .