QJEEM19Ma351c: JEE Main 2019 Mathematics - Class 11 JEEM19Ma351c Solution: All the points in the set S = { α + i α − i : α ∈ R } ( i = − 1 …

Question

Verified Solution • 2025–26 Session moderate

All the points in the set

S = {\frac{α + i}{α - i} : α \in R} (i = \sqrt{- 1})

lie on a :

Accepted Answer

Let h + ik =

\frac{α + i}{α - i}

=

\frac{(α + i) (α + i)}{(α - i) (α + i)}

=

\frac{(α^{2} - 1) + 2 i α}{α^{2} + 1}

∴

h =

\frac{α^{2} - 1}{α^{2} + 1}

and k =

\frac{2 α}{α^{2} + 1}

By squaring and adding we get

h² + k² = 1

∴

This is circle whose radius is 1.

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