Find the coordinates of a point whose distance from (3,5) is 5 and that from (0,1) is 10 units.

Asked by Somesh Meena | 7th Feb, 2014, 06:36: PM

Expert Answer:

Dear Student,

Please check your question if it is correct. The following is the solution provided but it needs some more information to complete this soluyion.

Let the coordinates of the point be (x, y)

Now, distance of (x, y) from the point (3, 5) is 5 units.

rightwards double arrow left parenthesis x minus 3 right parenthesis squared plus left parenthesis y minus 5 right parenthesis squared equals 5 squared rightwards double arrow x squared minus 6 x plus 9 plus y squared minus 10 y plus 25 equals 25

rightwards double arrow x squared plus y squared minus 6 x minus 10 y plus 9 equals 0............(1)

Also, distance of (x, y) from the point (0, 1) is 10 units.

rightwards double arrow left parenthesis x minus 0 right parenthesis squared plus left parenthesis y minus 1 right parenthesis squared equals 10 squared rightwards double arrow x squared plus y squared minus 2 y plus 1 equals 100

rightwards double arrow x squared plus y squared minus 2 y minus 99 equals 0...........(2)

Subtracting (2) from (1), we get

x squared plus y squared minus 2 y minus 99 minus x squared minus y squared plus 6 x plus 10 y minus 9 equals 0

rightwards double arrow 6 x plus 8 y minus 108 equals 0 rightwards double arrow 3 x plus 4 y equals 54..... left parenthesis 3 right parenthesis

Topper's Team


 

Let the coordinates of the point be (x, y)

Distance of (x,y) from the point (3,5) is 5 units.

http://www.meritnation.com/img/shared/discuss_editlive/4135575/2012_12_11_11_38_14/mathmlequation6601093341314430375.png 

and distance of (x,y) from the point (0,1) is 10 units.

http://www.meritnation.com/img/shared/discuss_editlive/4135575/2012_12_11_11_38_14/mathmlequation1127818620085897262.png 

subtracting equation (i) from (ii):

http://www.meritnation.com/img/shared/discuss_editlive/4135575/2012_12_11_11_38_14/mathmlequation8639897569133385796.png 

since 3x=2y put this in (iii)

http://www.meritnation.com/img/shared/discuss_editlive/4135575/2012_12_11_11_38_14/mathmlequation372960957334354787.png 

Answered by  | 7th Feb, 2014, 09:37: PM

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