A) Parabola
B) Ellipse
C) Circle
D) Pair of straight lines
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.
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