AP EAMCET · Maths · Complex Number
If \(z=x+i y\) and if the point \(\mathrm{P}\) in the Argand plane represents \(z\), then the locus of \(\mathrm{P}\) satisfying the equation \(|z-3 i|+|z+3 i|=10\) is
- A Circle with centre \((-3,3)\)
- B Hyperbola with eccentricity \(\frac{5}{3}\)
- C Ellipse with eccentricity \(\frac{3}{5}\)
- D Ellipse with eccentricity \(\frac{4}{5}\)
Answer & Solution
Correct Answer
(C) Ellipse with eccentricity \(\frac{3}{5}\)
Step-by-step Solution
Detailed explanation
\(|z-3 i|+|z+3 i|=10\) is an ellipse. \(2c = |3i - (-3i)| = 6 \Rightarrow c = 3\). \(2a = 10 \Rightarrow a = 5\). \(e = \frac{c}{a} = \frac{3}{5}\).
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