Use the information provided to write the standard form equation of each ellipse. 1) Vertices: (11, 0). (–11, 0) Foci: (2V10, 0). (-2 V10, 0) 2) Vertices: (0, 12). (0, –12). Foci: (0, 3 V15). (0. -3 V15)

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
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Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Writing Equations of Ellipses w/ Center (0, 0)
Recall the formulas for an ellipse with center (0, 0) are as
follows:
Ellipses with center (0, 0)
Standard equation
Vertices
(0, ta)
(+b, 0)
(ta, 0)
(0, +b)
(tc, 0)
Pythagorean Relation a= b² + c²a² = b² + c²
Co-Vertices
Foci
(0, ±c)
Our objective is going to be, given the foci and one other
property of the ellipse, we are going to write the equation of the
ellipse.
Use the information provided to write the standard form
equation of each ellipse.
1) Vertices: (11, 0), (–11, o)
Foci: (2 V10, 0). (-2 V10, 0)
2) Vertices: (0, 12), (0, –12).
Foci: (0, 3 V15), (0. –3 V15)
Use the information provided to write the general conic form
equation of each ellipse.
3) Vertices: (7, 0), (–7, 0)
Foci: (3 V5, 0), (-3 V5,0)
4) Vertices: (0, 9), (0, –9)
Foci: (0, 3 V5), (0, –3 V5)
Transcribed Image Text:Writing Equations of Ellipses w/ Center (0, 0) Recall the formulas for an ellipse with center (0, 0) are as follows: Ellipses with center (0, 0) Standard equation Vertices (0, ta) (+b, 0) (ta, 0) (0, +b) (tc, 0) Pythagorean Relation a= b² + c²a² = b² + c² Co-Vertices Foci (0, ±c) Our objective is going to be, given the foci and one other property of the ellipse, we are going to write the equation of the ellipse. Use the information provided to write the standard form equation of each ellipse. 1) Vertices: (11, 0), (–11, o) Foci: (2 V10, 0). (-2 V10, 0) 2) Vertices: (0, 12), (0, –12). Foci: (0, 3 V15), (0. –3 V15) Use the information provided to write the general conic form equation of each ellipse. 3) Vertices: (7, 0), (–7, 0) Foci: (3 V5, 0), (-3 V5,0) 4) Vertices: (0, 9), (0, –9) Foci: (0, 3 V5), (0, –3 V5)
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