I have written the correct question.This is from S chand sample papers. Is there any other way to prove m=l, so that we can prove mx=ly If the distance of P(x,y) from A(l+m, l-m) and B (l-m, l+m) are equal, prove that mx=ly

Asked by Divyaa | 24th Mar, 2017, 11:39: AM

Expert Answer:

Hi Divya,
 
We have checked our solution. It seems fine. 
We have also understood how to obtain mx=ly.
You need to change the x-coordinate of the point B, which should be m-l and NOT l-m.
For this problem, you will surely get x = y only.
You can refer to the following link for this question too. It has appeared in CBSE 2016 board paper.
The solution is there too, and you will see that ,
the point B, which should be m-l and NOT l-m.
 
http://www.topperlearning.com/study/cbse/class-10/mathematics/previous-year-question-papers/b101c2s3e8
 
It is similar to Question Number 13.
If the point P(x, y) is equidistant from the points A(a + b, b – a) and B(a – b, a + b). Prove that bx = ay.
Only in place of a they took m and in place of b they took l.

begin mathsize 16px style straight P left parenthesis straight x comma straight y right parenthesis comma space straight A left parenthesis straight l plus straight m comma space straight l minus straight m right parenthesis space and space straight B space left parenthesis straight l minus straight m comma space straight l plus straight m right parenthesis space
To space prove space colon space mx equals ly
Using space distance space formula comma
PA equals PB space... left parenthesis given right parenthesis
rightwards double arrow square root of left parenthesis straight l plus straight m minus straight x right parenthesis squared plus left parenthesis straight l minus straight m minus straight y right parenthesis squared end root equals square root of left parenthesis straight l minus straight m minus straight x right parenthesis squared plus left parenthesis straight l plus straight m minus straight y right parenthesis squared end root
Squaring space both space sides comma space we space get
left parenthesis straight l plus straight m minus straight x right parenthesis squared plus left parenthesis straight l minus straight m minus straight y right parenthesis squared equals left parenthesis straight l minus straight m minus straight x right parenthesis squared plus left parenthesis straight l plus straight m minus straight y right parenthesis squared
rightwards double arrow straight l squared plus straight m squared plus straight x squared plus 2 lm minus 2 lx minus 2 mx plus straight l squared plus straight m squared plus straight y squared minus 2 lm minus 2 ly plus 2 my
equals straight l squared plus straight m squared plus straight x squared minus 2 lm minus 2 lx plus 2 mx plus straight l squared plus straight m squared plus straight y squared plus 2 lm minus 2 ly minus 2 my
rightwards double arrow negative 2 mx plus 2 my equals 2 mx minus 2 my
rightwards double arrow 4 mx equals 4 my
rightwards double arrow straight x equals straight y end style

Answered by Rebecca Fernandes | 24th Mar, 2017, 11:12: PM

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