# Cassini ovals — parametric equation?

• Oct 5th 2012, 07:51 PM
ZeroDivisionError
Cassini ovals — parametric equation?
Anybody know the parametric form of an equation for a Cassini oval?
• Oct 5th 2012, 08:20 PM
Prove It
Re: Cassini ovals — parametric equation?
• Oct 5th 2012, 09:11 PM
MaxJasper
Re: Cassini ovals — parametric equation?
Cassini Oval in simple form of complex variables z, q1, q2:

$\displaystyle |z-\text{q1}| |z-\text{q2}|=b^2$

http://mathhelpforum.com/attachment....1&d=1349500197
• Oct 7th 2012, 11:30 AM
ZeroDivisionError
Re: Cassini ovals — parametric equation?
Thank you all for your help, but I don't know how to derive an equation of the form x(t) = |insert function of t|, y(t) = |insert function of t| from an equation in terms of x and y. Sorry, my friends; I'm going to have to ask for the explicit equations.
• Oct 7th 2012, 12:58 PM
MaxJasper
Re: Cassini ovals — parametric equation?
Cassini Oval: Parametric Equation

$\displaystyle x(\text{t})\text{=}\sqrt{\frac{m}{2}} \cos (t)$

$\displaystyle y(\text{t})\text{=}\sqrt{\frac{m}{2}} \sin (t)$

$\displaystyle m\text{=}2 \sqrt{\left(b^4-a^4\right)+a^4 \cos ^2(2 t)}+2 a^2 \cos (2 t)$

$\displaystyle 0<t\leq 2\pi$ and a<b

If a>b, this parametric equation generates only parts of Cassini Oval.
• Oct 7th 2012, 01:08 PM
skeeter
Re: Cassini ovals — parametric equation?
Cartesian to polar to parametric form ...

http://online.redwoods.cc.ca.us/inst...en/CalcPpr.pdf