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QJEEAdv07Mabf02: JEE Advanced 2007 Mathematics - Class 12 JEEAdv07Mabf02 Solution: Let be such that . Column (A) If and then (B) If and then (C)…

Let (x,y)(x, y) be such that sin⁡−1(ax)+cos⁡−1(y)+cos⁡−1(bxy)=π2{\sin ^{ - 1}}\left( {ax} \right) + {\cos ^{ - 1}}\left( y \right) + {\cos ^{ - 1}}\left( {bxy} \right) = {\pi \over 2} .

Column II
(A) If a=1a=1 and b=0,b=0, then (x,y)(x, y)
(B) If a=1a=1 and b=1,b=1, then (x,y)(x, y)
(C) If a=1a=1 and b=2,b=2, then (x,y)(x, y)
(D) If a=2a=2 and b=2,b=2, then (x,y)(x, y)

Column IIII
(p) lies on the circle x2+y2=1{x^2} + {y^2} = 1
(q) lies on (x2−1)(y2−1)=0\left( {{x^2} - 1} \right)\left( {{y^2} - 1} \right) = 0
(r) lies on y=xy=x
(s) lies on (4x2−1)(y2−1)=0\left( {4{x^2} - 1} \right)\left( {{y^2} - 1} \right) = 0

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