For the circle x2+y2=r2, find the value of r for which the area enclosed by the tangents drawn from the point P(6,8) to the circle and the chord of contact is maximum.
A
5
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
6
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
8
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is C5 Let the angle between the tangents is θ⟹tanθ2=r√62+82−r2
⟹sinθ2=r10,cosθ2=√100−r210
Area of triangle is 12(√S11)2sinθ=r(100−r2)3/2100
Let f(x)=r(100−r2)3/2⟹f′(x)=(100−r2)1/2(100−4r2)=0⟹r2=25⟹r=5