Maharashtra BoardEnglish MediumSTD 12 ScienceMathsPair of Straight Lines2 Marks
MCQ
The equation $\sqrt{(x-2)^2+y^2}+\sqrt{(x+2)^2+y^2}=4$ represents a
A
Circle
✓
Pair of straight lines
C
Parabola
D
Ellipse
✓
Answer
Correct option: B.
Pair of straight lines
(B) $\sqrt{(x-2)^2+y^2}+\sqrt{(x+2)^2+y^2}=4$ i.e. $\sqrt{(x-2)^2+y^2}=4-\sqrt{(x+2)^2+y^2}$ Squaring both sides, we get $(x-2)^2+y^2=16-8 \sqrt{(x+2)^2+y^2}+(x+2)^2+y^2$ $\Rightarrow x^2-4 x+4+y^2=16+x^2+4 x+4+y^2$ $-8 \sqrt{(x+2)^2+y^2}$ $\Rightarrow x+2=\sqrt{(x+2)^2+y^2}$ Again squaring both sides, we get $(x+2)^2=(x+2)^2+y^2$ $\Rightarrow y^2=0$ This is an equation of pair of two coincident straight lines.
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