Find the cartesian equation of the curve whose parametric equations are
`x = a + c cos alpha, y = b + c sin alpha , 0 le alpha < 2pi`.

Find the equation of the following curve : x=a+c cos alpha, y=b+c sin alpha , where 0 le alpha< 2 pi , in cartesian form*. In case the curve is a circle, find its centre and radius.

Find the equation of the circle whose centre is (a cos alpha, a sin alpha) and radius is a.

Find the equations of the following curves in cartesian form. Wherever the curve is a circle, find its centre and radius : x= 7+4 cos alpha, y= -3+4 sin alpha , where 0le alpha <2 pi .

An equation of a circle touching the axes of coordinates and the line x cos alpha+ y sin alpha = 2 can be

Find A^2 if A = [(cos alpha, sinalpha),(-sin alpha, cos alpha)]

Find the equations of the following curves in cartesian form. Wherever the curve is a circle, find its centre and radius : x=3 cos alpha, y=3 sin alpha .

Find the equations of the following curves in cartesian form. Wherever the curve is a circle, find its centre and radius : x=1+2 cos alpha, y=3+2 sin alpha .

Find the equations of the following curves in cartesian form. Wherever the curve is a circle, find its centre and radius : x=5+3 cos alpha, y=7+3 sin alpha .

One side of a square makes an angle alpha with x axis and one vertex of the square is at origin. Prove that the equations of its diagonals are x(sin alpha+ cos alpha) =y (cosalpha-sinalpha) or x(cos alpha-sin alpha) + y (sin alpha + cos alpha) = a , where a is the length of the side of the square.

If sin (3alpha) /cos(2alpha) < 0 If alpha lies in