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Home / Doubts and Solutions/JEE/Mathematics

SHOW THAT THE PATH OF A MOVING POINT SUCH THAT ITS DISTANCES FROM TWO LINES 3x-2y=5
AND 3x+2y=5 ARE EQUAL IS A LINE.

Asked by neeraj.unnao 14th November 2016, 4:36 PM
Answered by Expert
Answer:
Given space two space lines space are comma 3 straight x space minus space 2 straight y space equals space 5........... left parenthesis straight i right parenthesis 3 straight x space plus space 2 straight y space equals space 5........... left parenthesis ii right parenthesis Let space straight P left parenthesis straight h comma space straight k right parenthesis space be space the space moving space point space such space that space its space distance space from space given space two space lines space is space equal. rightwards double arrow fraction numerator open vertical bar 3 straight h minus 2 straight k minus 5 close vertical bar over denominator square root of 9 plus 4 end root end fraction equals fraction numerator open vertical bar 3 straight h plus 2 straight k minus 5 close vertical bar over denominator square root of 9 plus 4 end root end fraction rightwards double arrow open vertical bar 3 straight h minus 2 straight k minus 5 close vertical bar equals open vertical bar 3 straight h plus 2 straight k minus 5 close vertical bar rightwards double arrow 3 straight h minus 2 straight k minus 5 minus 3 straight h minus 2 straight k plus 5 equals 0 rightwards double arrow negative 4 straight k equals 0 rightwards double arrow straight k space equals space 0 Put space straight k space equals space 0 space in 3 straight h minus 2 straight k minus 5 space equals space 0 space we space get comma 3 straight h minus space 0 space minus 5 space equals 0 straight h equals 5 over 3 Thus space the space point space straight P left parenthesis 5 over 3 comma space 0 right parenthesis space space is space equidistant space from space both space the space lines. Also space we space can space see space that space it space represents space the space equation space of space straight a space straight space line space where space straight x space equals space 5 over 3 space and space straight y space equals space 0. So space the space path space of space straight a space moving space point space satisfing space given space conditions space is space straight a space straight space line.
Answered by Expert 15th November 2016, 10:57 AM
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