JEE PYQ: Parabola Question 6
Question 6 - 2020 (02 Sep Shift 2)
The area (in sq. units) of an equilateral triangle inscribed in the parabola $y^2 = 8x$, with one of its vertices on the vertex of this parabola, is:
(1) $64\sqrt{3}$
(2) $256\sqrt{3}$
(3) $192\sqrt{3}$
(4) $128\sqrt{3}$
Show Answer
Answer: (3)
Solution
Let $A = (2t^2, 4t)$ and $B = (2t^2, -4t)$. For equilateral triangle with vertex at origin: $\tan 30° = \frac{4t}{2t^2} \Rightarrow t = 2\sqrt{3}$. Area $= \frac{1}{2} \cdot 8(2\sqrt{3}) \cdot 2 \cdot 24 = 192\sqrt{3}$.
BETA
