Complex Numbers And Quadratic Equations question 679
Question: The locus of a point in the Argand plane that moves satisfying the equation $ |z-1+i|-|z-2-i|=3: $
Options:
A) is a circle with radius 3 and centre at $ z=\frac{3}{2} $
B) is an ellipse with its foci at $ 1-i $ and $ 2+i $ and major axis $ =3 $
C) is a hyperbola with its foci at $ 1-i $ and $ 2+i $ and its transverse axis $ =3 $
D) None of the above
Show Answer
Answer:
Correct Answer: C
Solution:
The given eq. implies that the difference between the distances of the moving point from two fixed points (1 - i) and (2 + i) is constant using the property of the hyperbola that the difference between the focal distances of any point on the curve is constant, the locus in reference is therefore a hyperbola.
BETA
