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If the point (5,4) and (x,y) are equidistant from the point (4,5) , prove that X square + Y square - 8 x minus 10 Y + 39 = 0

If the point (5,4) and (x,y) are equidistant from the point (4,5) , prove that X square + Y square - 8 x minus 10 Y + 39 = 0

Grade:10

2 Answers

Arun
25757 Points
3 years ago
5,4) and ( x,y) are equidistant from (4,5)
So the distance between (5,4) and ( 4,5) is equal to distance  (x,y) and (4,5)
So using distance formula we have :
√{(5-4)2 + (4-5)2} = √{(x-4)2 + (y-5)2 }
√2 = √ {x2 +16 -8x + y2 +25 -10y}
Squaring both sides we get :
2 = {x2 +16 -8x + y2 +25 -10y}
Or x2 +16 -8x + y2 +25 -10y -2 = 0
Or x2  -8x + y2  -10y +39 = 0 ( hence proved)
Saurabh Koranglekar
askIITians Faculty 10335 Points
3 years ago
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