y² Let S be the set S = {(x, y) | 62 (Hint: Consider how to define an ellipse by its foci ?) ≤1}. Show that S is a convex set.

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter12: Conic Sections
Section12.1: Parabolas
Problem 1E: A parabola is the set of all points in the plane that are equidistant from a fixed point called the...
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5. A subset A of R" is convex if for every two points u, v in A, the line segment tu+(1-t)v,
0 ≤ t ≤ 1 is contained in A.
y²
Let S be the set S =
+ <1}. Show that S is a convex set.
6²
(Hint: Consider how to define an ellipse by its foci ?)
a²
{(x, y) |
Transcribed Image Text:5. A subset A of R" is convex if for every two points u, v in A, the line segment tu+(1-t)v, 0 ≤ t ≤ 1 is contained in A. y² Let S be the set S = + <1}. Show that S is a convex set. 6² (Hint: Consider how to define an ellipse by its foci ?) a² {(x, y) |
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