A) x = 0
B) y = 0
C) x + y = 0
D) x-y = 0
Correct Answer: B
Solution :
We have, \[x=t\cos t\]and \[y=t\sin t\] \[\therefore \] \[\frac{dx}{dt}=\cos t-t\sin t\] and \[\frac{dy}{dt}=\sin t+t\operatorname{cost}\] At the origin, we have \[x=0,y=0\] \[\Rightarrow \] \[t\cos t=0\] and \[t\sin t=0\] \[\Rightarrow \] \[t=0\] The slope of the tangent at \[t=0\]is \[\frac{dy}{dx}={{\left( \frac{dy/dt}{dx/dt} \right)}_{t=0}}={{\left( \frac{\sin t+\cos t}{\cos t-t\sin t} \right)}_{t=0}}=0\] So, the equation of the tangent at the origin is \[y-0=0(x-0)\]\[\Rightarrow \]\[y=0\]
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