Conic Sections Question 169
An equilateral triangle is inscribed in the parabola $ y^{2}=4ax $ with its vertices lying on the parabola, then the length of its side is equal to
Options:
8a
B) $ 8a\sqrt{3} $
C) $ a\sqrt{2} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ L_1=\sqrt{3}y-x=0 $ , solving $ L_1 $
and $ S_1\equiv y^{2}-4ax=0 $
Then $ y=4a\sqrt{3} $ and $ x=12a $
Hence $ L=\sqrt{144a^{2}+48a^{2}} $
$ =a\sqrt{192}=8a\sqrt{3} $ .
BETA
