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Medium Equation of a circle when the endpoints of a diameter are given MCQs for JEE

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Part of Co-ordinate Geometry in JEE Main Mathematics.

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Q1MathsUnit 10: Co-ordinate Geometry
Let A(1,2)\mathbf{A}(\mathbf{1}, \mathbf{2}) and B(3,4)\mathbf{B}(\mathbf{3}, \mathbf{4}) be two points. Let C(x,y)\mathbf{C}(x, y) be a point such that (x−(x- 1) (x−3)+(y−2)(y−4)=0.(x-3)+(y-2)(y-4)=0 . If area of (ΔABC)=1,(\Delta A B C)=1, then the maximum number of positions of C\mathbf{C} in xy\boldsymbol{x} \boldsymbol{y} -plane is

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