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1984年高考数学试题(理科)第六题(2)小题为“求经过定点M(1,2),以y轴为准线,离心率为1/2的椭圆的左顶点的轨迹方程。”高考标准答案中给出了利用椭圆定义推导的唯一解答,其过程虽较简单,但方法灵活,不易掌握,今试用双参数来解此题。解:如图,设左顶点为A_1(x,y),中心是o′(h,k),因e=c/a=1/2, ∴ a=2c,得b~2=3c~2, 又左准线为y轴, h=a~2/c=4c,
In the 1984 Mathematics Exam Question (Science) Question 6 (2), the title was “Let the trajectory equation of the left vertex of the ellipse whose eccentricity is 1/2 with the fixed point M (1,2) and the y-axis as the guideline. ”The answer to the college entrance examination standard gives the only solution to the derivation of ellipse definitions. Although the process is relatively simple, the method is flexible and not easy to grasp. We will try to solve this problem using two parameters. Solution: As shown in the figure, set the left vertex to A_1(x,y) and the center to o′(h,k), because e=c/a=1/2, ∴ a=2c, get b~2=3c~2 , And the left guideline is the y axis, h=a~2/c=4c,