Question

Consider two particles moving in the xyxy-plane according to parametric equations.

At time tt, the position of particle A is given by x(t) = 2t-3, y(t) = t^2-3t-5x

Let kk be some real number. At time tt, the position of particle B is given by x(t) = 4t+3, y(t) = 2t+k^2x

Think about the curve traced out by the movement of particle A. Find the equation of the tangent line to the curve at t=4t=4. Give your answer in slope-intercept form, y=mx+by=mx+b.

At any point, is there a horizontal tangent line to the curve traced out by the movement of particle A? If so, give the (x,y)(x,y)-coordinates of the position of the curve where the horizontal tangent line occurs. If not, explain why.

Is there a value for the real number k for which Particles A and B will collide? If so, give a value of kk. If not, clearly explain your reasoning why. In either case, remember to show work to support your answer.

Answer 1