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

Question

The area (in sq. units) of an equilateral triangle inscribed in the parabola y2=8 x, with one of its vertices on the vertex of this parabola, is : (A) 64 √3 (B) 256 √3 (C) 192 √3 (D) 128 √3

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/a492e014dddc829ec7df1a3f92ffe5d4-.png" /> tan 30°=(4 t /2 t 2)=(2/ t ) ⇒ t =2 √3 AB =8 t =16 √3 Area =256.3 ⋅ (√3/4)=192 √3

Q. The area (in sq. units) of an equilateral triangle inscribed in the parabola $y^{2} = 8 x,$ with one of its vertices on the vertex of this parabola, is :

$643$

$2563$

$1923$

$1283$

$tan 3 0^{\circ} = \frac{4 t}{2 t ^{2}} = \frac{2}{t} \Rightarrow t = 23$
$A B = 8 t = 163$
Area $= 256.3 \cdot \frac{3}{4} = 1923$

Q. 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 :

643​

2563​

1923​

1283​