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Q.
The number of points of intersection of $| z -(4+3 i )|=2$ and $| z |+| z -4|=6, z \in C$ is :
JEE MainJEE Main 2022Complex Numbers and Quadratic Equations
Solution:
$C:(x-4)^{2}+(y-3)^{2}=4$
$E: \frac{(x-2)^{2}}{9}+\frac{y^{2}}{5}=1$
Lower Extremity of vertical diameter of circle $\rightarrow(4,1)$
Put in ellipse $\Rightarrow \frac{(4-2)^{2}}{9}+\frac{1}{5}-1$
$=\frac{4}{9}+\frac{1}{5}-1$
$=\frac{29}{45}-1 < 0$
Two Solution
