JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let \(z \in C\) the set of complex numbers. Then the equation, \(2\left| {z + 3i} \right| - \left| {z - i} \right| = 0\) represents
- A a circle with radius \(\frac{8}{3}\)
- B a circle with diameter \(\frac{10}{3}\)
- C an ellipse with length of major axis \(\frac{16}{3}\)
- D an ellipse with length of minor axis \(\frac{16}{9}\)
Answer & Solution
Correct Answer
(A) a circle with radius \(\frac{8}{3}\)
Step-by-step Solution
Detailed explanation
Let \(z=x+i y\) \(\Rightarrow 2|x+i(y+3)=| x+i(y-1) |\) \(\Rightarrow 2 \sqrt{x^{2}+\left(y+3^{2}\right)}\) \(=\sqrt{x^{2}+\left(y-1^{2}\right)}\) \(\Rightarrow 4 x^{2}+4(y+3)^{2}=x^{2}+(y-1)^{2}\) \(\Rightarrow \quad 3 x^{2}=y^{2}-2 y+1-4 y^{2}-24 y-36\)…
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