Question

If the coordinates of a point be given by the equation $x=a(1-cos\theta ),y=asin\theta$, then the locus of the point will be

• A. A straight line
• B. A circle
• C. A parabola
• D. An ellipse

Answer 1

The correct option is B

A circle

On eliminating \theta, we get the required locus.

Since $x=a(1-cos\theta )\Rightarrow x-a=-acos\theta$ .................(i)

and $y=asin\theta$ ................(ii)

Now adding the squares of (i) and (ii), we get

$x^2+y^2-2ax=0$, which is equation of a circle.