Complex Numbers And Quadratic Equations question 340
Question: If z is a complex number in the Argand plane, then the equation $ |z-2|+|z+2|=8 $ represents [Orissa JEE 2004]
Options:
A) Parabola
B) Ellipse
C) Hyperbola
D) Circle
Show Answer
Answer:
Correct Answer: B
Solution:
$ |z-2|+|z+2|\ =8 $
Þ $ \sqrt{{{(x-2)}^{2}}+y^{2}}+\sqrt{{{(x+2)}^{2}}+y^{2}}=8 $
Þ $ x^{2}+y^{2}+4-4x=64+x^{2}+y^{2}+4+4x $ $ -16\sqrt{{{(x+2)}^{2}}+y^{2}} $
Þ $ -8x-64=-16\sqrt{{{(x+2)}^{2}}+y^{2}} $
Þ $ (x+8)=2\sqrt{{{(x+2)}^{2}}+y^{2}} $
Þ $ x^{2}+64+16x=4[x^{2}+y^{2}+4+4x] $
Þ $ 3x^{2}+4y^{2}-48=0 $
$ \Rightarrow \frac{x^{2}}{16}+\frac{y^{2}}{12}=1 $ , which is an ellipse.
BETA
