PUMaC 2013 · 团队赛 · 第 3 题
PUMaC 2013 — Team Round — Problem 3
题目详情
- The area of a circle centered at the origin, which is inscribed in the parabola y = x − 25, can a be expressed as π , where a and b are coprime positive integers. What is the value of a + b ? b m
解析
- The area of a circle centered at the origin, which is inscribed in the parabola y = x − 25, can a be expressed as π , where a and b are coprime positive integers. What is the value of a + b ? b 2 2 2 SOLUTION: Let the equation of the circle be x + y = r . The discriminant of the quadratic 99 2 2 2 equation y = ( r − y ) − 25 is 0. This gives r = so that a + b = 103. 4 ANSWER: 103 m