May 10th, 2017, 01:41 AM  #1 
Member Joined: Jan 2016 From: Blackpool Posts: 40 Thanks: 0  ellipse question
Let γ : R → R 2 be the plane curve given by γ(t) = (3 tanh t, 2 sech t). Show that the image of γ is contained in an ellipse, and determine the equation of the ellipse. Is the image the whole ellipse? 
May 10th, 2017, 03:33 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 17,919 Thanks: 1383 
As tanh²t + sech²t ≡ 1, an equation for the ellipse is (x/3)^2 + (y/2)^2 = 1. As sech t > 0, the image isn't the whole ellipse. 

Tags 
ellipse, question 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
A question about an ellipse  bach71  Calculus  1  March 21st, 2013 09:32 AM 
Ellipse question  indianmathnoob  Algebra  1  April 24th, 2012 04:12 AM 
Ellipse question (eccentricity e.t.c)  pre exam  master555  Algebra  4  January 13th, 2012 08:29 AM 
Ellipse Ellipse Intersection  tom9000  Algebra  1  June 17th, 2009 01:40 PM 
Ellipse question (eccentricity e.t.c)  pre exam  master555  Applied Math  0  December 31st, 1969 04:00 PM 