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二次曲线上四点共圆问题是高考常考内容,2016年高考四川卷文科第20题,2011年高考全国大纲卷理科第21题,2005年高考湖北卷理科第21题以及2002年江苏卷、广东卷第20题都是关于二次曲线上四点共圆的问题。下面是二次曲线上四点共圆的一个简洁充要条件:
The four-point common-circle problem on the quadratic curve is the content of the regular entrance examination for the college entrance examination. The 20th item of the Sichuan Encyclopedia of Liberal Arts in the 2016 college entrance examination, the 21st item of the National Outline Colledge of the College Entrance Examination in 2011, the 21st item of the 2005 Wuhan College Entrance Examination, and the 2002 Jiangsu volume The 20th question in the Guangdong issue is about the four-point common-circle problem on the quadratic curve. The following is a concise and necessary condition for the four-point co-circularity on the quadratic curve: