Find the point(s) on the ellipse x = 3 cost, y = sin t, 0 less than or equal to t less than or equal to 2pi closest to the point(4/3,0) (Hint: Minimize the square of the distance as a function of t.) The point(s) on the ellipse closest to the given point is(are) . (Type ordered pairs. Use a comma to separate answers as needed.)

Answer and Step-by-step explanation:

The computation of points on the ellipse is shown below:-

Distance between any point on the ellipse

To minimize

Now we create a table by applying the critical points which are shown below:

t            

0          

When t = , x is and y is . So, the required points are

When t = , x is and y is . So, the required points are

4 puzzles in 3 hours

step-by-step explanation:

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50