Question

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

• A. $\sqrt { 3 }$/2
• B. 4$\sqrt { 3 }$/2
• C. 8$\sqrt { 3 }$/2
• D. 8$\sqrt { 3 }$

Answer 1

Answer: (D)

8$\sqrt { 3 }$

Answer 2

Let A be the vertex and ABC be the equilateral triangle inscribed in the parabola y² = 4x, AM be perpendicular on BC.

Then if AB = l, AM = l cos 30⁰

And BM = l sin 30⁰.

Thus the coordinates of B are (l$\sqrt { 3 }$/2, l/2)

Since B lies on the parabola y² = 4x

Ž (l/2)² = 4l$\sqrt { 3 }$/2

Ž l = 8$\sqrt { 3 }$.