Find the Curvature k and the radius of curvature R for y= ex. Find the center of the circle of curvature at the point (0,1)

Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle rolls along the x -axis given that P is at a maximum when x=0.

Suppose that the circle with center 0, 0 and radius length r contains the point a,b. Find the slope of the tangent line to the circle at the point a,b.