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The position of paint P is r=a cos theta...

The position of paint P is r=a cos `thetahati+b sin thetahatj`, where a and b ar constants and `theta` is angle between r and x axis . If the rate of increasing of `theta` Is `omega` Find the equation of path of particle.

A

Circle

B

Parabola

C

Ellipse

D

Stratight line

Text Solution

Verified by Experts

(c) `:. r=xhati+yhatj" " r=xi+j`
But `r=a cos thetahati+bsin theta`
`:." " x=acos theta`
`y=b sin theta`

`:.(x^(2))/(a^(a))+(y^(2))/(b^(2))=cos^(2) theta+sin^(2)theta=1`
`(x^(2))/(a^(2))+(y^(2))/(b^(2))=`
This is an equation of ellipse.
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