The number of points of intersection of |z-(4+3i)|=2 and |z|+|z-4|=6, z C, is

Question

The number of points of intersection of $|z-(4+3i)|=2$ and $|z|+|z-4|=6,\ z\in\mathbb C$, is

Accepted Answer

${C_1}:|z - (4 + 3i)| = 2$ and ${C_2}:|z| + |z - 4| = 6$, $$z \in C$$

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$$\sqrt5$$ and (4, 2) lies inside the both C1 and C2 and (4, 3) lies outside the C2

$$\therefore$$ number of intersection points = 2

Solutions · 1