Hyperbolic line!

Calculus Level 5

as the GIF above the stick might be considered as a line fastened on the disk circumference .

the disk radius is 1meter length.

u is the directing vector of the line .

r,t are the radius, circle tangent directing vectors.

the resulting shape formula using the disk center as reference of the coordinates...

\( c\frac{(y-y_0 )^2}{a^2} +\frac{(x-x_0)^2}{b^2} =1\)

what is \( 10((ab)^2 -c+\sqrt{2}y_0-x_0) \) ?

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