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Find the coordinates of a point which is at a distance of 2units from (5,4) and 10units from (11,-2).

Find the coordinates of a point which is at a distance of 2units from (5,4) and 10units from (11,-2).
 

Grade:11

1 Answers

Vikas TU
14149 Points
4 years ago
Let that point be (x,y)
Then from distance formulae:
4 = (x-5) ^2 + (y-4)^2.............(1)
100 = (x-11)^2 +  (y+2)^2...............(2)
Solving the eqns. (1) and (2) we get,
x – y + 1 = 0
or the coordinates we get are = > (x , x+1)
Now restart to any point find the dstance,
that is:
(x-5)^2 + (x + 1 – 4) ^2 = 4
or
(x-5)^2 + (x-3)^2 = 4
x^2 – 8x + 15 = 0 
we get x = 5 and x= 3
and y = 6 and y = 4

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