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Find the equation of the set of all points such that the difference
of their distance from (4,0) and (-4, 0) is always equal of 2 unit.
Identify the curve thus obtained.
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Answer:
Answer
It is given that the difference of the distance between the point (4,0) and (−4,0) is 2
Hence
(x−4)
2
+(y−0)
2
−
(x+4)
2
+(y−0)
2
=2
(x−4)
2
+(y)
2
=2+
(x+4)
2
+(y)
2
Squaring both sides, we get
(x−4)
2
+(y)
2
=4+(x+4)
2
+(y)
2
+4
(x+4)
2
+y
2
On expanding, we get
x
2
−8x+16+y
2
=4+x
2
+8x+16+y
2
+4
(x+4)
2
+y
2
−16x−4=4
(x+4)
2
+y
2
−4(4x+1)=4
(x+4)
2
+y
2
−(4x+1)=
(x+4)
2
+y
2
Squaring both sides, we get
16x
2
+8x+1=x
2
+8x+16+y
2
15x
2
−y
2
=15
Dividing throughout by 15, we get
1
x
2
−
15
y
2
=1
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