A) \[(a,\text{ }0)\]
B) \[(0,\text{ }a)\]
C) (0, 0)
D) \[(a,\text{ }a)\]
Correct Answer: A
Solution :
We have, \[x=a(1+\cos \theta ),y=a\sin \theta \] \[\frac{dx}{d\theta }=a(-\sin \theta ),\frac{dy}{d\theta }=a\cos \theta \] \[\Rightarrow \] \[\frac{dy}{dx}=\frac{dy/d\theta }{dx/d\theta }=-\frac{\cos \theta }{\sin \theta }\] \[\therefore \]Equation of normal at\[[a(1+\cos \theta ).a\sin \theta ]\] \[(y-a\sin \theta )=\frac{\sin \theta }{\cos \theta }[x-a(1+\cos \theta )]\] It is clear that in the given options normal passes through the point (a, 0).
You need to login to perform this action.
You will be redirected in
3 sec
