4. Let P be any point on the ellipse E: x²y² + = 1. 25 9 (i) Show that the equation of the tangent at P = (5 cos 0, 3 sin ) is 3x cos + 5y sin 0 = 15. (ii) Assume that 0 < 0 < π. The tangent at the vertex A = (5,0) on the major axis meets the tangent at P at the point R. If O is the origin, show that OR is parallel to A'P where A' = (-5, 0) the opposite vertex to A.
4. Let P be any point on the ellipse E: x²y² + = 1. 25 9 (i) Show that the equation of the tangent at P = (5 cos 0, 3 sin ) is 3x cos + 5y sin 0 = 15. (ii) Assume that 0 < 0 < π. The tangent at the vertex A = (5,0) on the major axis meets the tangent at P at the point R. If O is the origin, show that OR is parallel to A'P where A' = (-5, 0) the opposite vertex to A.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
(ii) only please
Transcribed Image Text:4. Let P be any point on the ellipse E:
25
= 1.
(i) Show that the equation of the tangent at P:
=
3x cos 0 + 5y sin 0
-
(5 cos 0, 3 sin 0) is
15.
(ii) Assume that 0 < 0 < π. The tangent at the vertex A = (5,0) on the major
axis meets the tangent at P at the point R. If O is the origin, show that OR
is parallel to A'P where A' = (–5,0) the opposite vertex to A.
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
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
