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Analytic Geometry Problem

Source: 1993 National High School Mathematics League, Exam One, Problem 4

February 27, 2020
analytic geometrygeometry

Problem Statement

C:(x−arcsin⁡a)(x−arccos⁡a)+(y−arcsin⁡a)(y+arccos⁡a)=0C:(x-\arcsin a)(x-\arccos a)+(y-\arcsin a)(y+\arccos a)=0. The length of string of CC cut by l:x=π4l:x=\frac{\pi}{4} is dd. When aa changes, the minumum value of dd is (A)π4(B)π3(C)π2(D)π\text{(A)}\frac{\pi}{4}\qquad\text{(B)}\frac{\pi}{3}\qquad\text{(C)}\frac{\pi}{2}\qquad\text{(D)}\pi
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