The auxiliary circle of a family ofellipses passes through the origin and makes intercepts of 8 units and 6 units on the x-and y-axes, respectively. If the eccentricity of all such ellipses is 1/2, then find the locus of the focus.
The auxiliary circle of a family ofellipses passes through the origin and makes intercepts of 8 units and 6 units on the x-and y-axes, respectively. If the eccentricity of all such ellipses is 1/2, then find the locus of the focus.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.2: Ellipses
Problem 31E
Related questions
Question
a.The auxiliary circle of a family ofellipses passes through the origin and makes intercepts
of 8 units and 6 units on the x-and y-axes, respectively. If the eccentricity of all such
ellipses is 1/2, then find the locus of the focus.
b. Find the area of the greatest rectangle that can be inscribed in the ellipse \frac{x\power{2}|a\power{2}}+\frac{y\power{2}|b\power{2}}=1.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning