Question

Find the point on the ellipse x = 2cos(t), y = sin(t), 0 ≤ t ≤ 2π closest to the point (3/4, 0). (Hint: Minimize the square of the distance as a function of t.)

Name: find the point on the ellipse x 2costy sint0 t 2 closest to the point 34 0 hint minimize the square of the distance as a function of t 05804
Uploaded: 2023-08-17T02:32:01-08:00
Duration: 3 min 26 s
Channel: Zack A
Description: find the point on the ellipse x 2costy sint0 t 2 closest to the point 34 0 hint minimize the square of the distance as a function of t 05804

          Find the point on the ellipse x = 2cos(t), y = sin(t), 0 ≤ t ≤ 2π closest to the point (3/4, 0). (Hint: Minimize the square of the distance as a function of t.)

Added by Brenda H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Zack A

08/17/2023

Step 1

The distance formula in the plane is \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\), where \((x_1, y_1)\) and \((x_2, y_2)\) are two points in the plane. For our case, \((x_1, y_1) = (3/4, 0)\) and a point on the ellipse is given by \((x_2, y_2) = (2\cos(t), Show more…

Show all steps

Thanks for your feedback!

Find the point on the ellipse x = 2cos(t), y = sin(t), 0 ≤ t ≤ 2π closest to the point (3/4, 0). (Hint: Minimize the square of the distance as a function of t.)