Question
Question: The locus represented by the complex equation \|z – 2 – i\| = \|z\| sin \(\left( \frac{\pi}{4} - \ar...
The locus represented by the complex equation |z – 2 – i| = |z| sin (4π−argz)is the part of –
A
A pair of straight lines
B
A circle
C
A parabola
D
A rectangular hyperbola
Answer
A parabola
Explanation
Solution
Sol. Let z = x + iy = r (cos q + i sin q), then the equation is
| (x – 2) + i(y – 1)| = r (21cosθ−21sinθ)
= 21 (r cos q – r sin q)
or (x−2)2+(y−1)2 = 21 (x – y).
which is the part of a parabola with focus (2, 1) and directrix x – y = 0.