Show that the point `(x, y)` , where `x=5 cos theta, y=-3+5 sin theta`, lies on a circle for all values of `theta

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

If x=r cos theta,y=r sin theta, show that

prove that all lines represented by the equation : (2 cos theta + 3 sin theta) x + (3 cos theta - 5 sin theta) y- (5 cos theta - 2 sin theta) = 0 pass through a fixed point for all values of theta . Find the coordinates of that point.

The line (x-1) cos theta + (y-1) sin theta =1, for all values of theta touches the circle

Show that the centroid of the triangle with vertices (5 cos theta, 4 sin theta), (4 cos theta, 5 sin theta) and (0, 0) lies on the circle x^(2)+y^(2)=9 .

Show that : x=a cos theta - b sin theta and y = a sin theta + b cos theta , represent a circle where theta is the parameter.

Find the fix point through which the line (2cos theta+3sin theta)x+(3cos theta-5sin theta)y-(5cos theta-2sin theta)=0 passes for all values of theta

Show that equations x=a cos theta + b sin theta, y = a sin theta - b cos theta represents a circle, wheter theta is a parameter.

Show that the normal at any point theta to the curve x=a cos theta+a theta sin theta,y=a sin theta-a theta cos theta is at a constant distance from the origin.