8#
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小 發表於 2014-10-29 04:57 AM (第 3438 天)
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2 tangents from (-2,1) to unit circle centre (0,0) Obviously upper one is horizontal i.e. slope=0 so max value =0
the lower tangent slanting downward from L to R has minimum slope (-ve)
let -x be angle turning from the upper tangent clockwise (-ve) to the line joining (-2,1) to (0,0)
noting radius is perpendicular to tangent and noting the 2 equivalent triangles and tan x = 1/2
so minimum slope tan (-2x) = 2(-1/2)/[1-(-1/2)^2] = -4/3 so min value = -4/3
This requires very little computation, one can actually get the answer with mental calculation!