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以椭圆、双曲线的两个焦点F_1,F_2及异于长轴、实轴端点的点P为顶点构成的△F_1PF_2就是椭圆、双曲线的焦点三角形。我们可以利用焦点三角形的特殊性解决两类圆锥曲线问题。1求点P的坐标问题在椭圆、双曲线的焦点三角形中,两焦点的坐标是明确的,唯一需要指定或计算坐标的就是点P了。例1双曲线(x~2)/(16)-(y~2)/9=1上的点P到点(5,0)的
△ F_1PF_2, which is composed of the two focal points F_1 and F_2 of ellipse and hyperbola and the point P which is different from the end point of the long axis and the real axis, is the focal triangle of the ellipse and the hyperbola. We can use the particularity of the focus triangle to solve two types of conic problems. 1 find the coordinates of the point P In the oval, hyperbolic focus triangle, the coordinates of the two focal points is clear, the only need to specify or calculate the coordinates is the point P. Example 1 Point P on hyperbolic line (x ~ 2) / (16) - (y ~ 2) / 9 = 1 to