If the locus of z C, such that ((z-1)/(2z + i)) + ((z-1)/(2z - i)) = 2, is a circle of radius r and center (a,b), then 15ab/(r²) is equal to:

Complex Numbers and Quadratic Equations: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q161

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

If the locus of

z \in \mathbb{C}

, such that

\Re\bigl(\tfrac{z-1}{2z + i}\bigr) + \Re\bigl(\tfrac{\overline{z}-1}{2\overline{z} - i}\bigr) = 2

, is a circle of radius

r

and center

(a,b)

, then

\tfrac{15ab}{r^2}

is equal to: