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我们知道,经过圆的x~2+y~2=R~2上任意一点P(x_0,y_0)的切线方程为:x_0x+y_0y=R~2记住并直接利用这个公式,能加快解题速度,收到事半功倍的效果,它的证明较易,本文从略。下面举一例说明。例:求过点(3,4)且到原点距离为5的直线方程。解;依题意知:所求直线到原点距离为5,因此,此直线可看成是过圆x~2+y~2=25上一点P(3,4)的一条切线,故此直线方程为: 3x+4y=25 细心的同学会发问:如果这点P(x_0,y_0)不在圆上,那么方程:x_0x+y_0y=R~2的几何意义又是什么呢? 下面着重谈谈这个问题: 首先,我们设P(x_0,y_0)在定圆x~2+y~2
We know that the tangent equation of P(x_0, y_0) at any point on the circle x~2+y~2=R~2 is: x_0x+y_0y=R~2 Remember and use this formula directly to speed up the problem solving Speed, the effect of getting a multiplier, it is easier to prove, this article is abbreviated. Here is an example. Example: Find the linear equation of point (3,4) and the distance to the origin of 5. Solution; according to the topic of knowledge: the distance from the straight line to the origin is 5, therefore, the straight line can be seen as a tangent line of a point P(3,4) on the circle x~2+y~2=25, so the line equation For: 3x+4y=25 Careful classmates ask: If this point P(x_0, y_0) is not on the circle, then what is the geometric meaning of the equation: x_0x+y_0y=R~2? The following focuses on this issue : First, let’s set P(x_0,y_0) in the circle x~2+y~2