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所谓圆锥曲线的焦点弦,就是一直线经过圆锥曲线的焦点且与圆锥曲线相交于两点所成的线段。焦点弦弦长公式可由下面的定理和推论给出。定理苦e是圆锥曲线的离心率,p是焦点到准线的距离,则与圆锥曲线的对称轴的夹角为θ的焦点弦的长为:l=2ep/(1-e~2cos~2θ) 证明:如图1, 以圆锥曲线的焦点F为极点O,焦点向准线所作垂线的反向延长线为极轴建立极坐标系,则圆锥曲线的极坐标方程
The focus chord of the so-called conic curve is the line segment that the straight line passes through the focal point of the conic curve and intersects the conic curve at two points. The focal chord length formula can be given by the following theorems and inferences. The theorem bitter e is the eccentricity of the conic section, p is the distance from the focal point to the quasi-line, and the length of the focal chord with the angle θ of the symmetry axis of the conic section is: l=2ep/(1-e~2cos~2θ Proof: As shown in Fig. 1, the focal point F of the conic curve is the pole O, and the reverse extension line of the perpendicular line to the directivity line is the polar axis. The polar coordinate equation of the conic curve is established.