题目246：椭圆的切线

欧拉计划

Tangents to an ellipse

A definition for an ellipse is:
Given a circle c with centre M and radius r and a point G such that d(G,M)<r, the locus of the points that are equidistant from c and G form an ellipse.

The construction of the points of the ellipse is shown below.

Given are the points M(-2000,1500) and G(8000,1500).
Given is also the circle c with centre M and radius 15000.
The locus of the points that are equidistant from G and c form an ellipse e.
From a point P outside e the two tangents t₁ and t₂ to the ellipse are drawn.
Let the points where t₁ and t₂ touch the ellipse be R and S.

For how many lattice points P is angle RPS greater than 45 degrees?

题目：

椭圆的定义为：
给定一个以 M 的圆心，半径为 r 的圆 c 以及点 G，其中 d(G,M) 椭圆上点的构造如下所示。

给定点 M(-2000,1500) 和 G(8000,1500)。
给定以 M 为圆心，半径为 15000 的圆 c。
到点 G 和圆 c 距离相等的点的位置构成椭圆 e。
从椭圆 e 外一点 P 向椭圆作两条切线 t₁ 和 t₂。
设切线 t₁ 和 t₂ 与椭圆相切于点 R 和 S。

求有多少格点 P 使得角 RPS 大于 45 度？