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JEE MainMathematicsEasyComplex Numbers

If a > 0 and the equation
∣z−a2∣+∣z−2a∣=3\left| z - a^{2} \right| + |z - 2a| = 3 represents an ellipse, then
complete set of values of a is

Show answer and solution
∣a2−2a∣<3\left| a^{2} - 2a \right| < 3
−3<a2−2a<3⇒−1<a<3- 3 < a^{2} - 2a < 3 \Rightarrow - 1 < a < 3 but a>0a > 0
∴a∈(0,3)\therefore a \in (0,3)

Source: Grass-G / M-18 Mathematics Paper 27 Nov Third.docx

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