'ind a path in R² whose image set is: (a) The circle with radius 4 and center at (-1, 3). (b) The ellipse which in Cartesian coordinates has the equation, 72 = 1. 9. 25 (c) The branch of the hyperbola, x2 = 1 9. 16 lying in the lower-left quadrant (x, y) < 0. +

'ind a path in R² whose image set is: (a) The circle with radius 4 and center at (-1, 3). (b) The ellipse which in Cartesian coordinates has the equation, 72 = 1. 9. 25 (c) The branch of the hyperbola, x2 = 1 9. 16 lying in the lower-left quadrant (x, y) < 0. +

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Rational Functions And Conics

Section4.3: Conics

Problem 98E

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Question

Please solve (c) by finding a vector valued function f(t)=(x(t),y(t)) that has the image set in the question

Find a path in R? whose image set is:
(a) The circle with radius 4 and center at (-1,3).
(b) The ellipse which in Cartesian coordinates has the equation,
,2
= 1.
25
(c) The branch of the hyperbola,
x2
y2
= 1
9
16
lying in the lower-left quadrant (x, y) < 0.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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An ellipse is the set of all points in the plane for which the ____ of the distances from two fixed points F1 and F2 is constant. The points F1 and F2 are called the ____ of the ellipse.
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