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How to find the pQ of ellipse
Find pQ by ellipse: the same circle is in an ellipse or the ellipse is in a circle, so the value of PO is the largest, the value of P'o is the smallest, and the value of PO is also the largest when the ellipse intersects the circle, and P'o = 0. (Here, p and p' refer to the coordinates when δ = 0).

Solve the elliptic equation and concentric circle equation simultaneously, and get the coordinate p of the inscribed point. The distance from the center of the circle to the tangent point PO plus R (the radius of the original circle) is the maximum value of P'Q', and the distance from the tangent point P' to the center of the circle P' O is subtracted from R (the radius of the original circle), that is, P' Q' is the minimum value of two curves. I said that it is the nature of the tangent point and the circle (the distance between any point on the circle and the center of the circle is equal, all of which are R).

Introduction to ellipse

In mathematics, an ellipse is a curve around two focal points on a plane, so for each point on the curve, the sum of the distances to the two focal points is constant. Therefore, it is a generalization of a circle, and it is a special type of ellipse with two focuses at the same position. The shape of an ellipse (how to "stretch") is expressed by its eccentricity, which can be any number from 0 (the limit case of a circle) to close to but less than 1.