State the geometrical meaning of the constants involved in `x cos alpha + y sin alpha = p`

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

Prove that the area of the parallelogram formed by the lines x cos alpha+y sin alpha=p ,x cos alpha+y sin alpha=q , x cos beta+y sin beta=r and x cos beta+y sin beta=s is ±(p−q)(r−s)cosec(α−β).

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 .

Find the intercepts on the axes made by the straight lines : x cos alpha+y sin alpha=sin2 alpha .

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

Locus of the point of intersection of lines x cosalpha + y sin alpha = a and x sin alpha - y cos alpha =b (alpha in R ) is

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.

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 the straight lines ax+by+c=0 and x cos alpha +y sin alpha = c enclose an angle pi//4 between them and meet the straight line x sin alpha - y cos alpha = 0 in the same point , then

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