Question

If the parametric equation of a circle being $x=2+3\cos t$, $y=-5+3\sin t$, find the equation of circle.

Answer 1

Given, the parametric equation of the circle is $x=2+3\cos t$.......(1), $y=-5+3\sin t$.......(2).

From (1) we have,

$\cos t=\frac{x-2}{3}$......(3).

And from the equation (2) we get,

$\sin t=\frac{y+5}{3}$.......(4).

Since,

${\cos }^{2}t+{\sin }^{2}t=1$

or, ${\left(\frac{x-2}{3}\right)}^2+{\left(\frac{y+5}{3}\right)}^2=1$

or, $(x-2{)}^2+(y+5{)}^2=3^2$.

This is the required equation of circle.