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 inclination to the x-axis of the lines : x cos alpha+y sin alpha=p .

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 .

Find the derivatives of the following : 3 sin x + 2 sin alpha , where alpha is a constant.

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 .

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 .

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.

Show that the point (x,y), where : x=a+r cos alpha, y=b+r sin alpha lie on a circle for all values of alpha .

Find the locus of middle points of the variable line x cos alpha+y sin alpha-p=0 intercepted by the axes given that p remains constant .