The equation $\sqrt{(x-2)^2+y^2}+\sqrt{(x+2)^2+y^2}=4$, where $-2 < x < 2$, represents a
The equation $\sqrt{(x-2)^2+y^2}+\sqrt{(x+2)^2+y^2}=4$, where $-2 < x < 2$, represents a
Circle
Pair of lines
Parabola
Line segment
Solution
Given,
$
\sqrt{(x-2)^2+y^2}+\sqrt{(x+2)^2+y^2}=4
$
According above equation
Let
$
\begin{aligned}
P & =(x, y) \\
A & =(2,0) \\
B & =(-2,0)
\end{aligned}
$
From Eq. (i)
$
P A+P B=A B
$
$\Rightarrow$ Eq. $A, P, B$ are collinear
$\Rightarrow$ Eq. (i) represents a line segment
Hence, option (4) is correct