Question
Mathematics Question on complex numbers
The number of points of intersection of |z – (4 + 3i)| = 2 and |z| + |z – 4| = 6, z ∈ C, is
A
0
B
1
C
2
D
3
Answer
2
Explanation
Solution
The correct answer is (C) : 2
C1 : |z – (4 + 3i)| = 2 and C2 : |z| + |z – 4| = 6, z ∈ C
C1: represents a circle with centre (4, 3) and radius 2 and C2 represents a ellipse with focii at (0, 0) and (4, 0) and length of major axis = 6, and length of semi-major axis 2√5 and (4, 2) lies inside the both C1 and C2 and (4, 3) lies outside the C2
Fig.
Therefore,
no. of intersection points = 2