Q. 134.8( 4 Votes )

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Answer :

Given:


Two lines 3x – 2y = 5 and 3x + 2y = 5


To prove:


The path of a moving point such that its distances from two lines 3x – 2y = 5 and 3x + 2y = 5 are equal is a straight line


Concept Used:


Distance of a point from a line.


Explanation:


Let P(h, k) be the moving point such that it is equidistant from the lines 3x 2y = 5 and 3x + 2y = 5



|3h – 2k – 5| = |3h + 2k – 5|


3h – 2k – 5 = ±(3h + 2k – 5)


3h – 2k – 5 = 3h + 2k – 5 and 3h – 2k – 5 = -3h + 2k – 5


k = 0 and 3h = 5


Hence proved, the path of the moving points are 3x = 5 or y = 0. These are straight lines.


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