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Question: Answered & Verified by Expert
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
MathematicsStraight LinesAP EAMCETAP EAMCET 2019 (20 Apr Shift 2)
Options:
  • A an ellipse
  • B a parabola
  • C a line segment
  • D a circle
Solution:
1533 Upvotes Verified Answer
The correct answer is: a line segment
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.

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