A) 3
B) 5
C) \[\frac{3}{5}\]
D) 15
E) 4
Correct Answer: D
Solution :
Given curve is \[{{x}^{2}}+xy+{{y}^{2}}=7\] On differentiating w.r.t.\[x,\] \[\Rightarrow \]\[2x+x\frac{dy}{dx}+y+2y\frac{dy}{dx}=0\] \[\Rightarrow \] \[(x+2y)\frac{dy}{dx}=-(2x+y)\] \[\Rightarrow \]\[{{\left( \frac{dy}{dx} \right)}_{(1,-3)}}=\frac{-(2-3)}{(1-6)}=-\frac{1}{5}\] \[\therefore \]Length of subtangent\[=\frac{y}{\frac{dy}{dx}}=\frac{-3}{\frac{1}{-5}}=15\]You need to login to perform this action.
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