a) OA=1+4cot⁡θ      OB=4+tan⁡θOA+OB=5+4cot⁡θ+tan⁡θ       ≥5+24cot⁡θtan⁡θ=5+(2×2)=9b) Reflection of P (4, -1) in y = x is Q (-1,4). Hence,     PQ=(4+1)2+(−1−4)2=50=52 c)  AB=22 and ⋅OC=2      Maximum value of d is OF=2+22=32d) The given line is      x=4+12y+12⇒y=2x−9      Hence, the intercept made by x -axis is 92