Cassini ovals — parametric equation?

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October 5th 2012, 07:51 PM
ZeroDivisionError

Cassini ovals — parametric equation?

Anybody know the parametric form of an equation for a Cassini oval?
October 5th 2012, 08:20 PM
Prove It

Re: Cassini ovals — parametric equation?

Cassini oval - Wikipedia, the free encyclopedia
October 5th 2012, 09:11 PM
MaxJasper

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Re: Cassini ovals — parametric equation?

Cassini Oval in simple form of complex variables z, q1, q2:

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

http://mathhelpforum.com/attachment....1&d=1349500197
October 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.
October 7th 2012, 12:58 PM
MaxJasper

Re: Cassini ovals — parametric equation?

Cassini Oval: Parametric Equation

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

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

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

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

If a>b, this parametric equation generates only parts of Cassini Oval.
October 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

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