Conic Sections Question 177
Question: Equation $ \sqrt{{{(x-2)}^{2}}+y^{2}}+\sqrt{{{(x+2)}^{2}}+y^{2}}=4 $ represents
[Orissa JEE 2004]
Options:
A) Parabola
B) Ellipse
C) Circle
D) Pair of straight lines
Show Answer
Answer:
Correct Answer: D
Solution:
Given equation is, $ \sqrt{{{(x-2)}^{2}}+y^{2}}+\sqrt{{{(x+2)}^{2}}+y^{2}}=4 $
$ \sqrt{{{(x-2)}^{2}}+y^{2}}=4-\sqrt{{{(x-2)}^{2}}+y^{2}} $
Squaring both sides, we get $ \sqrt{{{(x+2)}^{2}}+y^{2}}=x+2 $
Again squaring both sides, we get $ y^{2}=0 $ , which is the equation of pair of straight lines.
BETA
