The locus of a point $P(x, y)$ satisfying the equation $\sqrt{(x-2)^2+y^2}+\sqrt{(x+2)^2+y^2}=4$, is
The locus of a point $P(x, y)$ satisfying the equation $\sqrt{(x-2)^2+y^2}+\sqrt{(x+2)^2+y^2}=4$, is
an ellipse
a parabola
a line segment
a circle
Solution
Given, equation
$
\sqrt{(x-2)^2+y^2}+\sqrt{(x+2)^2+y^2}=4
$
$\Rightarrow$ Sum of distance of a point $P(x, y)$ w.r.t. points $A(2,0)$ and $B(-2,0)=$ Distance between points $A(2,0)$ and $B((-2,0)$
$
\Rightarrow \quad A P+B P=A B
$
$\therefore$ Locus of point $P(x, y)$ is a line segment.
Hence, option (c) is correct