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Question

Find the locus of a point which moves so that the difference of its distances from the points, (5,0) and (−5,0) is 2 is:

A
x21+y224=1
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B
x224+y21=1
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C
x224−y22=1
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D
x21−y224=1
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Solution

The correct option is B x21−y224=1
The locus is nothing but hyperbola.
Difference of distance of a point from foci =2a
Given distance is 2⇒a=1
Distance between foci =2ae=2√a2+b2=√(5+5)2
⇒a2+b2=25
⇒b2=24
Therefore, locus is x21−y224=1

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