My Math Forum How to parametrize this curve?

 Algebra Pre-Algebra and Basic Algebra Math Forum

 May 31st, 2013, 07:17 PM #1 Newbie   Joined: May 2012 Posts: 17 Thanks: 0 How to parametrize this curve? Hi!, I have this plain curve given in polar coord. and I'm asked to parametrize it, but I really don't know where to start. Any advise? the equation is $r^2=(1+(1/2)r^2sen^2(t)) /(1-(3/4)cos^2(t))$ where t is the angle. Thanks!
 June 1st, 2013, 10:12 AM #2 Senior Member   Joined: Dec 2012 Posts: 372 Thanks: 2 Re: How to parametrize this curve? I believe you meant 'sin' instead of 'sen'. To begin solving your problem, first make $r^2$ the subject of the equation, thereby obtaining$r^2= \dfrac{4}{1 + sin^2 t}$. Afterwards, use the following identities for transformation into Euclidean coordinates: $r^2= x^2 + y^2$ and $t= \arctan$$\frac{y}{x}$$$. If you do your arithmetic right, you will then obtain the simplification; $x^2 + 2 y^2= 4$. You should recognize this to be the equation for an ellipse, which has the parametrization $f:[0 , 2\pi) \rightarrow \mathbb{R}^2 \ ; \ t \mapsto (2 cos t, \sqrt{2} sin t)$. You can easily check that this parametrization satisfies your Euclidean equation $x^2 + 2 y^2= 4$. Hope you understand and are satisfied with these tips.

 Tags curve, parametrize

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post fe phi fo Algebra 1 June 27th, 2012 10:34 AM mboricgs Algebra 8 May 26th, 2012 01:53 AM clandarkfire Algebra 2 November 22nd, 2011 05:27 PM Marin Advanced Statistics 0 March 30th, 2009 01:23 PM chrishaig Real Analysis 1 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top