Question

An object is moving in the plane according to the parametric equations

x(t)=8sin(π t)

y(t)=4cos(π t)

for 0 ≤ t ≤ 1

,where time units are seconds and units on the coordinate axes are feet. The path traveled by the object is a portion of an ellipse in the first quadrant, as pictured. The location of the object at time t will be denoted by P(t)=(x(t),y(t)). A laser beam projects from the object in a direction perpendicular to the tangent line along what is called a normal line. If t≠ 1/2, the normal line will cross the x-axis at a point (m(t), 0). .

a) When 0 ≤ t ≤ 1, the equation of the normal line to the path is

b) When t≠ 1/2, the formula for the coordinate m(t)=

c) lim t→1/2 m(t)=

Answer 1

Please UPVOTE if this answer helps you understand better.

Solution:-

Please UPVOTE if this answer helps you understand better.