An equilateral triangle is inscribed in the parabola y2 = 4x... | MATH - PARABOLA | SolveeIt | Solveeit

Today, August 18

Question

An equilateral triangle is inscribed in the parabola y² = 4x, whose one vertex is at the vertex of the parabola. The length of its side is

A

$4 \sqrt { 3 }$

B

$2 \sqrt { 3 }$

C

$16 \sqrt { 3 }$

D

$8 \sqrt { 3 }$

Answer

$8 \sqrt { 3 }$

Explanation

Solution

Let A = (at², 2at), B = (at², -2at) are the other two vertices of the equilateral triangle.

∴ tan30⁰ =

⇒ t = 2 $\sqrt { 3 }$

∴ The length of the side AB = 4at

= 4.2 $\sqrt { 3 }$

= 8 $\sqrt { 3 }$