Given, the equation of a Cartesian circle is given in this general formula: $(x-a)^2 + (y-b)^2 = r^2$. This can be derived from the distance formula and Pythagoras's Theorem. However, how can I derive the general formula of an ellipse: $\frac{(x-a)^2}{c} + \frac{(y+b)^2}{d} = 1$ ?

  • $\begingroup$ Take a circle and stretch one axis. The formula you have is not most general as you can also rotate an ellipse. $\endgroup$
    – user121049
    Jan 18, 2019 at 8:40
  • $\begingroup$ perhaps it might be good to include what do you think an ellipse is. $\endgroup$ Jan 18, 2019 at 9:50
  • $\begingroup$ en.wikipedia.org/wiki/Ellipse#Equation $\endgroup$ Jan 18, 2019 at 10:46
  • 1
    $\begingroup$ This depends on the definition of an ellipse you use. By the way your formula is not the general one. It describes only the ellipses with axes parallel to the coordinate ones. $\endgroup$
    – user
    Jan 18, 2019 at 13:03


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