Ex: Find the Rectangular and Polar Equation of a Circle From a Graph

This video explains how to determine the equation of a circle in rectangular form and polar form from the graph of a circle.

[jonnuki]

Why does the constant conveniently happen to cancel out with the 25 on the left expansion? Do we have an example where the constant doesn't cancel?

[uniqueHandle-dsffS]

Is it possible to rewrite this polar equation so that the r-coordinate is always non-negative? :)

[YES: r = sqrt(2) * 5 * sqrt{1 - 24/25 * sin(2 theta) - 7/25 * cos(2 theta)}, for some range of theta (if theta in [0, 2 pi] - there will be also second, symmetric, circle having S at [3, -4] ) ]

[federicogrande]

Me salvaste la vida, te quiero mucho 💚