wiki says eccentricity of a sliced conic section is sin(alpha)/sin(beta) without any explanation. Can someone derive this. alpha angle of cone

tombrooks

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wiki says eccentricity of a sliced conic section is sin(alpha)/sin(beta) without any explanation. Can someone derive this. alpha is angle of cone and beta is angle of slice or vise versa. I have never seen this in any book or other web site. This might be related to Daniel balls?
 
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