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文[1]中给出了圆锥曲线的一个性质定理(以椭圆为例):椭圆的三垂足定理如图1,过椭圆x2/a2+y2/b2=1(a>b>0)上任一点P作切线PL,又作PH⊥x轴交于H,过焦点F作FQ⊥PL交于Q,相应于焦点F的准线交x轴于G,则PQ/FQ=HQ/GQ.文[1]作者在证明该定理的过程中用到了三角形相似、四点共圆等几何方法,在处理椭圆切线时用到了导数、方程等代数方法.那么,能否利用椭圆切
In [1], a property theorem of conic is given (taking an ellipse as an example): The theorem of the three-foot ellipse of an ellipse is shown in Fig. 1. The over-elliptic x2 / a2 + y2 / b2 = 1 A point P for the tangential PL, but also for PH ⊥ x axis at H, over focus F for FQ ⊥ PL to Q, corresponding to the focus of the focal line F cross X axis in G, then PQ / FQ = HQ / GQ. [1] In the process of proving the theorem, the author used geometric methods such as triangular similarity and four-point total circle, and used algebraic methods such as derivatives and equations when dealing with elliptic tangent.