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 is a closed curve with two foci, where the sum of the distances from any point on the curve to the two foci is constant.
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 a pair of straight lines.
BETA
