JEE MAIN - Mathematics (2022 - 27th June Evening Shift - No. 1)
The number of points of intersection of
$$|z - (4 + 3i)| = 2$$ and $$|z| + |z - 4| = 6$$, z $$\in$$ C, is :
$$|z - (4 + 3i)| = 2$$ and $$|z| + |z - 4| = 6$$, z $$\in$$ C, is :
0
1
2
3
Explanation
$${C_1}:|z - (4 + 3i)| = 2$$ 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
_27th_June_Evening_Shift_en_1_1.png)
$$\therefore$$ number of intersection points = 2
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