Find the equation of the following curves in cartesian form. If the curve is a circle , then the find the centre and radius $x = - 1 + 2 cos a, y = 3 + 2 sin a$ $(0 ⩽ a < 2 π)$

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Solution

Given, $x = - 1 + 2 cos a$ and $y = 3 + 2 sin a$

${(\frac{x + 1}{2})}^{2} + (\frac{y - 3}{2}) = 1$

${(x + 1)}^{2} + {(y - 3)}^{2} = {(2)}^{2}$

From above equation we can see that it is a circle

Therefore,
$c e n t r e : - (1, 3)$
$r a d i u s : 2$

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