Differential Equations Question 204
Question: Orthogonal trajectories of family of the curve $ {x^{2/3}}+{y^{2/3}}={a^{2/3}} $ , where a is any arbitrary constant, is
Options:
A) $ {x^{2/3}}-{y^{2/3}}=c $
B) $ {x^{4/3}}-{y^{4/3}}=c $
C) $ {x^{4/3}}+{y^{4/3}}=c $
D) $ {x^{1/3}}-{y^{1/3}}=c $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ {x^{2/3}}+{y^{2/3}}={a^{2/3}} $ Or $ \frac{2}{3}{x^{-1/3}}+\frac{2}{3}{y^{-1/3}}\frac{dy}{dx}=0 $ Or $ \frac{dy}{dx}=-\frac{{x^{-1/3}}}{{y^{-1/3}}} $
…(1) Replacing $ \frac{dy}{dx}( \frac{\pi }{2}-\theta ) $ by $ -\frac{dx}{dy} $ , we get $ \frac{dx}{dy}=\frac{{x^{-1/3}}}{{y^{-1/3}}} $ Or $ \int{{x^{1/3}}dx=\int{{y^{1/3}}dy}} $ Or $ {x^{4/3}}-{y^{4/3}}=c $
BETA
