EllipseMedium

Question

If |z - 3 - i| + |z - 1 - 3i| = 3, then locus of z in argand plane is -

Options

A.line segment joining (3 + i) and (1 + 3i)
B.an ellipse with its foci (3 + i) and (1 + 3i)
C.an ellipse with its eccentricity and centre 2 + 2i.
D.perpendicular bisector of the line segment joining (3 + i) and (1 + 3i).

Solution

         
|z - (3 + i)| + |z - (1 + 3i)| = 3
PS1 + PS2 = 3 and S1 S2 = 2√2
⇒ Locus of P is ellipse with foci (1,3) and (3,1)
centre (2,2),e =

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