Deriving Lemniscate Locus Equation: Is It a Typo?

[ronaldor9]

Hello from the book I am reading it defines the lemniscate as the locus for which the product of the distances r₁ and r₂ with the coordinates x= a and x= -1 and y= 0 has the constant value of a².

I went about deriving the equation in polar coordinates from this locus, however I do not get the correct equation when the locus is defines as r₁ x r₂ = a² but when r₁ x r₂ = a the correct equation is arrived at.

Is this simply a typo on behalf of the author?

 

[tiny-tim]

Hello ronaldor9!

(try using the X² and X₂ tags just above the Reply box )

… however I do not get the correct equation when the locus is defines as r_1 x r_2 = a^2 but when r_1 x r_2 = a^2 the correct equation is arrived at.

erm … what's the difference?

 

[ronaldor9]

I went about deriving the equation in polar coordinates from this locus, however I do not get the correct equation when the locus is defines as r₁ x r₂ = a² but when r₁ x r₂ = a the correct equation is arrived at.

FIXED thanks!