Hello,
I try to understand the inverse of a line in a circle as described here -> https://i2.paste.pics/a96ec4e85e5f25c0080e978056bd1250.png
From my understanding [MATH]k^2 = r*r' [/MATH] hence he defined `r = k^2/(r')`. From this I would write `rcos(\theta) = (k^2 cos(\theta))/(r')` but author for some reason wrote this as [MATH]\frac{k^2r'cos\theta}{r'^2}[/MATH] (any idea why?)
The first serious question I have for the equation [MATH]c(X'^2+Y'^2) + 2k^2(gX' + fY') + k^4[/MATH] Author says it was derived by the multiplication of the equation for `C(X,Y) ` by `(X'^2 + Y'^2)` but I don't get that result. For example how he got `k^4` there?
Next, how he derived the formula for the R (radious of the new circle) [MATH]R'^2 = \frac{k^4(g^2+f^2)}{c^2} \cdot \frac{-k^4}{c}[/MATH]Likewise I dont get the center of the newly created circle (the one after the inversion) as `(-gk^2/c, -fk^2/c)` so multiplied by `k^2/c`. The `k^2 = r \cdot r'` and I don;t see the linkage with the center. I would rather say that the new center is `(-(g+c), -(f+sth))`
Thanks for the help.
I try to understand the inverse of a line in a circle as described here -> https://i2.paste.pics/a96ec4e85e5f25c0080e978056bd1250.png
From my understanding [MATH]k^2 = r*r' [/MATH] hence he defined `r = k^2/(r')`. From this I would write `rcos(\theta) = (k^2 cos(\theta))/(r')` but author for some reason wrote this as [MATH]\frac{k^2r'cos\theta}{r'^2}[/MATH] (any idea why?)
The first serious question I have for the equation [MATH]c(X'^2+Y'^2) + 2k^2(gX' + fY') + k^4[/MATH] Author says it was derived by the multiplication of the equation for `C(X,Y) ` by `(X'^2 + Y'^2)` but I don't get that result. For example how he got `k^4` there?
Next, how he derived the formula for the R (radious of the new circle) [MATH]R'^2 = \frac{k^4(g^2+f^2)}{c^2} \cdot \frac{-k^4}{c}[/MATH]Likewise I dont get the center of the newly created circle (the one after the inversion) as `(-gk^2/c, -fk^2/c)` so multiplied by `k^2/c`. The `k^2 = r \cdot r'` and I don;t see the linkage with the center. I would rather say that the new center is `(-(g+c), -(f+sth))`
Thanks for the help.
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