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For the circle x^2+y^2=r^2 ,find value of r for which area enclosed by tangents from P(6,8) and its chord of contact is maximum
ANS : 5 units
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4 Answers
1since OP=10 , sin(theta)=r/10 where theta belongs to (0,pi/2)
area = 1/2 x 2r x cos(theta) x (10-rsin(theta))
a= 10sin(theta)cos(theta)(10-10sin2theta))
a=100cos2thetaxsin(theta)xcos(theta)
da/dtheta =100[cos4(theta)-3sin2(theta)cos2(theta)}
=300cos4(theta)(1/√3-tan(theta))(1/√3+tan(theta))
a is maximum at theta =pi/6
r=10x1/2 = 5 units