Let equation of tangent be xcosα+ysinα=4
Now, its points of intersection with co-ordinate axis are
A(cosα4,0),P(0,sinα4)
Now, ar(ΔPAB)=2(arΔPAO)
=2×21(OA×OP)
=∣sinα4.cosα4∣=∣sin2α32∣≥32
which is maximum if, α=4π
∴P(0,sin4π4)
∴h=42
Let the tangents drawn to the circle, x2+y2=16 from the pointP(0,h) meet the x-axis at points A and B. If the area of ΔAPB is minimum, then positive value of h is:
Held on 10 Apr 2015 · Verified 6 Jul 2026.
42
32
43
33
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