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Question

The equation XY=1 is the new form of the equation xy3x+2y7=0, when the origin is shifted to the point Q. Find the co-ordinates of the point Q.

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Solution

xy3x+2y7=0
x(y3)+2y61=0
x(y3)+2(y3)=1
(x+2)(y3)=1 …………..(1) original equation
xy=1 ……….(2) Transformed equation
Let Q=(a,b)
If origin is shifted to (a, b)
X=xaandY=yb …………….(3)
Put (3) in (1)
We get (x+a+2)(y+b3)=1
but the final equation should be XY=1
on company, we have
a+2=0 and b3=0
a=2 and b=3
CoordinatesofQare(2,3).

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