JEE Mains · Maths · STD 11 - 4.1 complex nubers
The number of values of \(z \in \mathbb{C}\), satisfying the equations \(|z-(4+8i)|=\sqrt{10}\) and \(|z-(3+5i)|+|z-(5+11i)|=4\sqrt{5}\), is:
- A \(0\)
- B \(2\)
- C \(1\)
- D \(4\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
The first equation \(|z-(4+8i)|=\sqrt{10}\) represents a circle with center \(C(4, 8)\) and radius \(r = \sqrt{10}\). The second equation \(|z-(3+5i)|+|z-(5+11i)|=4\sqrt{5}\) represents an ellipse with foci at \(S_1(3, 5)\) and \(S_2(5, 11)\), and length of the major axis…
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