Applications-Of-Derivatives Question 471
Question: The angle of intersection of curves $ y=x^{2}, $ $ 6y=7-x^{3} $ at (1, 1) is
[Kurukshetra CEE 2002]
Options:
A) $ \pi /4 $
B) $ \pi /3 $
C) $ \pi /2 $
D) $ \pi $
Show Answer
Answer:
Correct Answer: C
Solution:
$ y=x^{2} $
Þ $ {{( \frac{dy}{dx} )}{(1,,1)}}=m_1=2x=2 $ $ 6y=7-x^{3}\Rightarrow 6,.,\frac{dy}{dx}=-3x^{2} $
Þ $ {{( \frac{dy}{dx} )}{(1,,1)}}=m_2=-\frac{1}{2} $ Clearly $ m_1m_2=-1, $ therefore angle of intersection is $ \frac{\pi }{2} $ .
BETA
