题目:设椭圆的中心是坐标原点,长轴在x轴上,离心率e=3~(1/3)/2,已知点P(0,3/2)到这个椭圆上的点的最远距离是7~(1/7),求这个椭圆的方程,并求椭圆上到点P的距离等于7~(1/7)的点的坐标. 这是一道高考题,当年不少同学的解法是这样的:依题意,作圆x2+(y-3/2)2=7,与椭圆方程联立;消去x,得 Title: Let the center of the ellipse be the origin of coordinates, the long axis on the x-axis, the eccentricity e=3~(1/3)/2, and the known point P(0,3/2) to the point on this ellipse The distance is 7~(1/7). Find the equation of this ellipse and find the distance from the ellipse to the point P equal to the coordinates of the 7~(1/7) point. This is a college entrance examination question, when many students were The solution is this: According to the meaning of the problem, make a circle x2+(y-3/2)2=7, which is in conjunction with the elliptic equation; eliminate x, get