A circle has a center at #(1 ,2 )# and passes through #(4 ,7 )#. What is the length of an arc covering #pi /4 # radians on the circle?

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Answer 1 · 2016-07-10T11:17:06

Length of Arc#=sqrt34*pi/4~=4.58unit#

Let us denote by #S# the Circle, by #r# radius, and pt.#C(1,2)#= Centre of #S#, and a pt #P(4,7)# on #S#

Then, dist. #CP=r,# and, using Dist. Formula, we get,

#r^2=CP^2=(4-1)^2+(7-2)^2=9+25=34#, giving #r=sqrt34#

The arc subtends angle #theta = pi/4# at the centre, so that,

Length of Arc#=r*theta=sqrt34*pi/4~=5.84*3.14/4=4.58unit#