The area (in sq.

Question

The area (in sq. units) of an equilateral triangle
inscribed in the parabola y2 = 8x, with one of
its vertices on the vertex of this parabola, is :

Accepted Answer

Let A = (2t2
, 4t)

B = (2t2
, -4t) (by symmetry as equilateral
triangle)

tan 30o = $$\frac{4t}{2t^{2}} $$ = $$\frac{2}{t} $$

$$ \Rightarrow $$ t = 2$$\sqrt{3} $$

AB = 8t = 16$$\sqrt{3} $$

Area of equilateral = $$\frac{1}{2} \times 16\sqrt{3} \times 24$$

= $$192\sqrt 3 $$

Solutions · 1