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解析几何问题的解题过程一般都比较繁琐,运算量较大,因此如何简化运算就成了同学们迫切要解决的问题。下面举例介绍一些简化解析几何题运算的办法,旨在提高同学们的解题速度。一、巧用定义例1已知⊙O方程为x~2+y~2=4,定点A(4,0)。求过点A且与⊙O相切的动圆圆心的轨迹方程。解析设动圆圆心P(x,y),即动点P满足几何关系:||PO|-|PA||=2,显然P点轨迹是以O、A为焦点,实轴在x轴上的双曲线,中心在OA中点
The problem-solving process of analyzing geometric problems is generally more complicated and computationally intensive, so how to simplify the operation has become an urgent problem to be solved by the students. Here are some examples to simplify the operation of the analytical method of solving the problem, designed to improve students’ problem solving speed. First, clever use of definition 1 known ⊙ O equation is x ~ 2 + y ~ 2 = 4, fixed point A (4,0). Find the trajectory equation of point A and tangent to ⊙O. P (x, y) is considered as the center point of the moving circle. That is, the moving point P satisfies the geometric relation: || PO | - | PA || = 2. Obviously the trajectory of point P is centered on O and A, Hyperbolic, center in the midpoint of OA