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Yes , thats true.
And besides its a basic question on locus.
The gen. strategy for such qns is to use the definition of that situation.Here the question talks about distances and them being equal.
So its natural to use distance formula on a variable point(h,k) , twice.
And then equate both , replace h>x , k>y .
Rearrange them to get it in the above form.
Sometimes a qn may ask a point which follows more constraints.Simply list out all the constraints , write them in mathematical form and try to create 1 eqn that links all of them.
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Moderation Team
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