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圆的切线的几何画法是大家熟悉的。我发现了另外三种圆锥曲线的切线的初等几何画法。一、作图 i)椭圆的切线的几何作图如图1,0为椭圆的中心,F_1、F_2为椭圆的焦点,P为椭圆外一点,过p作椭圆的切线。作法 1.以O为圆心,长半轴长a为半径作⊙O。 2.以PF_1(或PF_2)为直径作⊙O＇,交⊙O于Q、Q＇(若P在⊙O上,则Q、Q＇分别为以PF_1、PF_2为直径的圆与⊙O的另一交点)。 3.连PQ、PQ＇,则PQ、PQ＇就是所求作的切线。
The geometric drawing of the round tangent is familiar to everyone. I discovered the elementary geometry of the tangents of the other three conic curves. 1. Mapping i) The geometry of the tangent of the ellipse is shown in Fig. 1. 0 is the center of the ellipse, F_1, F_2 are the focus of the ellipse, P is the point outside the ellipse, and p is the tangent of the ellipse. Practice 1. Take O as the center of the circle, long axis length a is radius ⊙O. 2. Use PF_1 (or PF_2) as the diameter for ⊙O’, and intersect with O for Q, Q’ (if P is on ⊙O, then Q, Q’ are circles with diameter of PF_1, PF_2 and ⊙O. Another intersection). 3. With PQ and PQ’, PQ and PQ’ are the tangents to the demand.