Find what the following equations become when the origin is shifted to the point (1, 1)
(i) `x^2+xy-3x-y+2=0` (ii) `xy-y^2-x+y=0` (iii) `xy-x-y+1=0`
Text Solution
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The correct Answer is:
(i) `X^2+XY=0`
(ii) `XY−Y^2−Y=0`
(iii) `XY-1=0`
Let `(x,y)` be the old co-ordinates and `(X, Y)` be the new coordinates after shifting the origin to `(h,k)`.
Then `x=X+h, y=Y+k`.
Given origin is shifted to `(1,1)`.
`therefore h=1,\ k=1`
`x=X+1,y=Y+1`
(i) `x^2+xy-3x-y+2=0`
`(X+1)^2+(X+1)(Y+1)-3(X+1)-(Y+1)+2=0`
`X^2+1+2X+XY+X+Y+1-3X-3-Y-1+2=0`
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