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本文介绍解析几何中把参数方程化为普通方程的一些常用方法。 (一)代入法通过参数方程中的一个方程求出参数的表达式,把它代入另一方程,从而消去参数,化为普通方程。例1.化下列t为参数的方程为普通方程 x=at~2+2a (1) y=at~3+2at (2) 解:由(2),得y=t(at~2+2a)(3) 把(1)代入(3),得y=tx 即 t=y/x. (4) 把(4)代入(1),得x=ay~2/x~2+2a. 整理后,得ay~2=x~3-2ax~2. (二)同解方程变形法运用同解方程组的性质,消去参数。
This article describes some commonly used methods for parsing parameters into ordinary equations in analytic geometry. (a) Substitution method The expression of a parameter is obtained by an equation in the parametric equation, and it is substituted into another equation, thereby eliminating the parameter and converting it into a normal equation. Example 1. The following equation for t is the ordinary equation x=at~2+2a (1) y=at~3+2at (2) Solution: From (2), get y=t(at~2+2a) (3) Substituting (1) into (3) yields y = tx ie t = y/x. (4) Substituting (4) into (1) gives x=ay~2/x~2+2a. After that, get ay~2=x~3-2ax~2. (B) The solution of the same solution equation deformation method uses the same solution equations to eliminate the parameters.