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圆锥曲线的光学特性,不仅在工程技术上有着重要的实用价值,而且在数学解题中也得到广泛的应用。它的好处在于能减少计算量,使解题过程少而精,简而美。现举例赏析。例1 试证:抛物线的两条切线间的夹角等于过这两切点的两条焦半径的夹角的一半。分析:本题要证∠PAQ=(1/2)∠PFQ,我们将∠PFQ分解成∠PFX和∠QFX,它们分别是△PFT和△QFB的外角,而
The optical properties of conic curves not only have important practical value in engineering technology, but also have been widely used in mathematical problems. Its advantage is that it can reduce the amount of calculations, so that the problem-solving process is less sophisticated, simple and beautiful. Examples are now appreciated. Example 1 Testimonial: The angle between the two tangents of a parabola is equal to half of the angle between two focal radii passing through these two cut points. Analysis: This question is to prove that PAQ = (1/2) ∠ PFQ, we will ∠ PFQ decomposed into ∠ PFX and ∠ QFX, they are △ PFT and △ QFB external angle, and