Question 6. Recall that the distance between a point P and an object A is the minimum possible distance between P and a random point on A. Using this definition, find the distance between the point (0, 0) and the ellipse given by the parametric equation x(t) = 3 cost + 2 sint, y(t) = -3 cost + 2 sint by going through the steps as follows. (1) The distance by definition is the global minimum of f(x(t), y(t)), where f(x, y) is the distance between (0,0) and (x, y), namely f(x,y)=√x² + y² First, find the critical points of f(x(t), y(t)). (2) Then, find the global minimum of f(x(t), y(t)) by finding the minimum possible value attained by f(x(t), y(t)) at the critical points.
Question 6. Recall that the distance between a point P and an object A is the minimum possible distance between P and a random point on A. Using this definition, find the distance between the point (0, 0) and the ellipse given by the parametric equation x(t) = 3 cost + 2 sint, y(t) = -3 cost + 2 sint by going through the steps as follows. (1) The distance by definition is the global minimum of f(x(t), y(t)), where f(x, y) is the distance between (0,0) and (x, y), namely f(x,y)=√x² + y² First, find the critical points of f(x(t), y(t)). (2) Then, find the global minimum of f(x(t), y(t)) by finding the minimum possible value attained by f(x(t), y(t)) at the critical points.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Question 6. Recall that the distance between a point P and an object A is the minimum possible
distance between P and a random point on A. Using this definition, find the distance between
the point (0, 0) and the ellipse given by the parametric equation
x(t) = 3 cost + 2 sint, y(t) = 3 cost + 2 sint
by going through the steps as follows.
(1) The distance by definition is the global minimum of f(x(t), y(t)), where f(x, y) is the
distance between (0,0) and (x, y), namely
f(x, y) = √√√x² + y²
First, find the critical points of f(x(t), y(t)).
(2) Then, find the global minimum of f(x(t), y(t)) by finding the minimum possible value
attained by f(x(t), y(t)) at the critical points.
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