Applications Of Derivatives Question 54
Question: Area of the triangle formed by the normal to the curve $ x={e^{\sin ,}}^{y} $ at (1, 0) with the coordinate axes is:
Options:
A) ¼
B) ½
C) 3/4
D) 1
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ x={e^{\sin y}}\Rightarrow Inx=\sin y\Rightarrow \frac{1}{x}\frac{dx}{dy}=\cos y $
$ \therefore $ slope of normal at (1, 0) $ =-\frac{dx}{dy}=-1\times \cos 0=-1 $
$ \therefore $ Equation of normal is $ y-0=-1(x-1) $
$ \Rightarrow x+y=1 $ Which forms triangle of area $ \frac{1}{2} $ with axes.
BETA
