Question: If the coordinates of a point be given by the equation $x = a(1 - \cos\theta),y = a\sin\theta$, th...

Question

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

Answer 1

On eliminating θ, we get the required locus.

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

and $y = a \sin \theta$ .....(ii)

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

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

Question: If the coordinates of a point be given by the equation \(x = a(1 - \cos\theta),y = a\sin\theta\), th...