A) \[{{(abscissa)}^{2}}\]
B) \[{{(ordinate)}^{2}}\]
C) \[abscissa\]
D) \[ordinate\]
Correct Answer: C
Solution :
We have, \[{{x}^{m}}{{y}^{n}}={{a}^{m+n}}\] \[\Rightarrow \]\[m{{\log }_{e}}x+n{{\log }_{e}}y=(m+n){{\log }_{e}}a\] On differentiating both sides w.r.t. x, we get \[\Rightarrow \] \[\frac{m}{x}+\frac{n}{y}\cdot \frac{dy}{dx}=0\] \[\Rightarrow \] \[\frac{dy}{dx}=-\frac{my}{mx}\] \[\therefore \]Length of the subtangent\[=\left| \frac{y}{dy/dx} \right|\] \[=\left| -y\times \frac{nx}{my} \right|\] \[=\frac{n}{m}|x|\propto x\]
You need to login to perform this action.
You will be redirected in
3 sec
