Applications-Of-Derivatives Question 473
Question: For the curve $ xy=c^{2} $ the subnormal at any point varies as
[Karnataka CET 2003]
Options:
A) $ x^{2} $
B) $ x^{3} $
C) $ y^{2} $
D) $ y^{3} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ xy=c^{2} $ ?..(i) $ \because $ Subnormal = $ y\frac{dy}{dx} $ \ From (i), $ y=\frac{c^{2}}{x} $
Þ $ \frac{dy}{dx}=\frac{-c^{2}}{x^{2}} $ \Subnormal $ =\frac{y\times (-c^{2})}{x^{2}}=\frac{-yc^{2}}{{{( \frac{c^{2}}{y} )}^{2}}}=\frac{-yc^{2}y^{2}}{c^{4}}=\frac{-y^{3}}{c^{2}} $ \ Subnormal varies as $ y^{3}. $
BETA
