(x？ /a？ )+(y？ /b？ )= 1 (a>b>0)

Two foci F 1(-c, 0), F2(c, 0)

The two endpoints of the long axis A 1(-a, 0), A2(a, 0).

Because the point p is on the ellipse, it can be set to P(acost, bsint) and t ∈ r.

According to the formula of the distance between two points

|PF 1|？ =(acost+c)？ +(bsint)？

=a？ Because? t+2accost+c？ +b？ Sin? t

=(a？ -B? )cos？ t+2accost+c？ +b？

=c？ Because? t+2accost+a？

=(a+ccost)？

From-1≤cost≤ 1 and A > C > 0,

0； F 1F2(P is the point on the ellipse and f is the focus)

Let the two foci of an ellipse be F 1 and F2 respectively, and the distance between them is 2c. The sum of the distances from any point on the ellipse to F 1 and F2 is 2a (2a >: 2c).

Taking the straight line of F 1 and F2 as the X axis and the vertical line of the line segment F 1F2 as the Y axis, and establishing the rectangular coordinate system xOy, the coordinates of F 1 and F2 are (-c, 0) and (c, 0) respectively.

When the focus is on the X axis, the focus coordinate F 1(-c, 0)F2(c, 0).

When the focus is on the Y axis, the focus coordinate F 1(0, -c)F2(0, c).

Baidu Encyclopedia-Standard Equation of Ellipse