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Q.

A circle passing through the point  P(α,β)  in the first quadrant touches the two co-ordinates axes at the points A and B. The point P is above the line AB. The point Q on the line segment AB is the foot of perpendicular from P on AB. If PQ is equal to 11 units then the value of  2αβ= ___

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answer is 242.

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Detailed Solution

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Circle is  x2+y2−2rx−2ry+r2=0
P(α,β)  lies on it 
 P(α,β)………(1)
Equation of line AB is  x+y=r
Since d=11
|α+β−r|2=11  S.B.S
 α2+β2+r2+2αβ−2βr−2rα=2(121)
From (1)  0+2αβ=242   2αβ=242
   
 

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