抛物线光学性质 方程:

抛物线光学性质 解释和应用:

抛物线光学性质：从焦点发出的光线，经过抛物线反射后平行于抛物线的轴。

应用：探照灯、汽车前灯、卫星天线。抛物面反射镜将位于焦点的光源发出的光线汇聚成平行光束，用于远距离照明或信号传输。

证明：抛物线光学性质的微积分证明。

首先，设抛物线方程为 $y^2 = 4px$，焦点为 $F(p, 0)$。

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抛物线光学性质 图示:

抛物线光学性质 微积分证明:

微积分证明步骤：

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椭圆光学性质 方程:

椭圆光学性质 解释和应用:

椭圆光学性质：从一个焦点发出的光线，经过椭圆反射后汇聚到另一个焦点。

应用：回音廊、光学仪器、医疗设备（如碎石机）。椭圆反射镜将能量汇聚到另一个焦点，用于集中使用。

证明：椭圆光学性质的微积分证明。

首先，设椭圆方程为 $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$，焦点为 $F_1(-c, 0)$ 和 $F_2(c, 0)$。

Explanation part 1 Image:

椭圆光学性质 图示:

椭圆光学性质 微积分证明:

微积分证明步骤：

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双曲线光学性质 方程:

双曲线光学性质 解释和应用:

双曲线光学性质：从一个焦点发出的光线，经过双曲线反射后，其反射光线的反向延长线通过另一个焦点。

应用：卡塞格林天线、反射望远镜。双曲线反射镜反射来自一个焦点的光线，使其看起来像来自另一个焦点。

证明：双曲线光学性质的微积分证明。

首先，设双曲线方程为 $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$，焦点为 $F_1(-c, 0)$ 和 $F_2(c, 0)$。

Explanation part 1 Image:

双曲线光学性质 图示:

双曲线光学性质 微积分证明:

微积分证明步骤：

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