- Let be a horizontal line in the plane and
*F*(*r*,*s*) be a point not on that line. Let*e*>0 be a positive real number. Find an equation to describe all points*P*(*x*,*y*) such that the ratio of*PF*divided by the distance from*P*to equals*e*. What kind of curves do you get? - Let
*Q*(-*c*,0) and*R*(*c*,0) be given points on the*x*-axis. Find an equation to describe all points*P*(*x*,*y*) such that the sum of the distances*PQ*+*PR*is a constant. What kind of curves do you get? - Let
*Q*(-*c*,0) and*R*(*c*,0) be given points on the*x*-axis. Find an equation to describe all points*P*(*x*,*y*) such that the difference of the distances*PQ*-*PR*is a constant. What kind of curves do you get? - A wagon sits at the point (0,
*L*) and a child stands at the point (0,0), holding a rope of length*L*attached to the wagon. The child begins walking along the positive*x*-axis, pulling the wagon along with the rope. Find an equation to describe the curve that the wagon follows. - A wheel of radius
*a*rolls along the positive*x*-axis. There is a point*P*on the circumference of the wheel that initially touches the*x*-axis at the origin. Describe the curve traced out by*P*(*x*,*y*) as the wheel rolls, giving*x*and*y*in terms of the angle*t*about which the wheel has turned about its center. (Initially*t*=0. When*P*comes to rest on the*x*-axis again, .) - A string is wound tightly many times around a circle of radius
*a*centered at the origin. The end of the string is initially at the point (*a*,0). Describe the curve traced out by the end*P*(*x*,*y*) of the string as it is unwound, keeping the string taut. Let's assume that it is unwound in a counterclockwise direction. Suggestion: express the location of the point*P*in polar coordinates. Initially and*r*=*a*.

Wed Apr 21 08:26:07 EDT 1999