It is a long-standing problem to solve the maximum and minimum distance between a point outside the ellipse and a point on the ellipse. When studying conic in high school, I will dabble in this problem, but conventional thinking will step into the field of quartic equation with one variable. The extraordinary calculation of solving the quartic equation of one variable is daunting, and it can solve the problem in theory. There is no maneuverability, so I can only taste it. In this paper, the quadratic curve system and its degradation, the simplest form of univariate cubic equation and the factorization of bivariate quadratic polynomial in real domain are used to deal with it, thus avoiding the solution of univariate quartic equation, and actually expressing another way of solving univariate quartic equation by combining numbers and shapes.
This is my thesis. I can't come up with many formulas over ten pages here.
final conclusion
Judge the position relationship between point P and straight line y=xa/b, and substitute it into the corresponding formula to solve it.
I searched all over the internet, but I couldn't find the answer. Some time ago, I studied the solution of quartic equation in one variable, and saw another award-winning paper "A Preliminary Study on the Maximum Problem of the Distance from a Point Outside the Ellipse to the Ellipse" on the Internet, aiming at exploring the solution of quartic equation. But the final formula of this paper is wrong, and these two maximum problems have not been solved. Solving quartic equation across cubic equation should be a leap, so the conclusion is inevitable. Later I thought, since he didn't solve the problem, I wanted to see how to deal with it. Alas, I wasted a lot of time solving this problem, because I didn't know how to deal with it except quartic equation at school, so I wrote a paper to help my classmates who were as confused as me, and I needed detailed information to trust me privately.