A) \[y=x\]
B) \[y=-x\]
C) \[y=0\]
D) \[x=0\]
Correct Answer: C
Solution :
Given that, \[x=a(\theta -\sin \theta ),y=a(1+\cos \theta )\]On differentiating w.r.t. \[\theta \] respectively, we get \[\frac{dx}{d\theta }=a(1-\cos \theta ),\frac{dy}{d\theta }=a(-\sin \theta )\] \[\therefore \]\[\frac{dy}{dx}=\frac{-\sin \theta }{1-\cos \theta }\] For parallel curve, \[\frac{dy}{dx}=0\Rightarrow \theta =(2k+1)\pi .\] So, the tangent is parallel to x-axis ie, y = 0.You need to login to perform this action.
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