Question

The new origin so that the equation 2xy + 2x + 2y + 1 = 0 may be
translated to the form in which the first degree terms be missing, is​

Answer 1

Answer:

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Answer 2

Therefore the coordinate of the new origin is (-1,-1).

Step-by-step explanation:

Let, the origin was shifted to a point (a,b).

If (x',y') be the new coordinate of (x,y) with respect to the new origin, then

x=x'+a   and y= y'+b

Given equation is 2xy+2x+2y+1=0

Putting x=x'+a   and y= y'+b in the above equation

2(x'+a)(y'+b)+2(x'+a)+2(y'+b)+1=0

⇒2(x'y'+bx'+ay'+ab)+2x'+2a+2y'+2b+1=0

⇒2x'y'+(2b+2)x'+(2a+2)y'+2a+2b+1=0

Given that ,the first degree terms will be missing in the translated form of the new equation . It means the coefficient of x' and y' will be zero.

∴2b+2= 0

⇒2b=-2

⇒b= -1

and

2a+2=0

⇒2a=-2

⇒a=-1

Therefore the coordinate of the new origin is (-1,-1).