Search any question & find its solution
Question:
Answered & Verified by Expert
An equilateral triangle is inscribed in the parabola $y^2=8 x$, with one of its vertices is the vertex of the parabola. Then, length of the side of that triangle is
Options:
Solution:
2627 Upvotes
Verified Answer
The correct answer is:
$16 \sqrt{3}$ units
Let $a$ be the length of the side of an equilateral triangle.
Then, from above figure, we can say that the point $\left(\frac{\sqrt{3}}{2} a, \frac{a}{2}\right)$ will lie on parabola $y^2=8 x$.
So, $\left(\frac{a}{2}\right)^2=8\left(\frac{\sqrt{3}}{2} a\right) \Rightarrow a^2=16 \sqrt{3} a \Rightarrow a=16 \sqrt{3}$ units
Then, from above figure, we can say that the point $\left(\frac{\sqrt{3}}{2} a, \frac{a}{2}\right)$ will lie on parabola $y^2=8 x$.
So, $\left(\frac{a}{2}\right)^2=8\left(\frac{\sqrt{3}}{2} a\right) \Rightarrow a^2=16 \sqrt{3} a \Rightarrow a=16 \sqrt{3}$ units
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.