JEE Advanced Mathematics question
Match the statements in **Column I** with those in **Column II**. [**Note:** Here takes values in the complex plane and and denote the imaginary part and real part of respectively.] Column I: (A) The set of points satisfying is contained in or equal to (B) The set of points satisfying is contained in or equal to (C) If then the set of points is contained in or equal to (D) If then the set of points is contained in or equal to Column II: (p) an ellipse with eccentricity (q) the set of points satisfying (r) the set of points satisfying (s) the set of points satisfying (t) the set of points satisfying
Solution
**(A)** The condition says is equidistant from the points and . For these are distinct points on the imaginary axis, symmetric about , so lies on their perpendicular bisector, the real axis. ( also satisfies it and is real.) Equivalently, with $ = θ +
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