When applying a transformation to a curve, you substitute the inverse transformation into the curve's equation.

For translation by (h,k): replace x with X+h and y with Y+k in the equation. For rotation by theta: replace x with Xcos(theta)-Ysin(theta) and y with Xsin(theta)+Ycos(theta).

Example: To find the equation of x^{2+y}^2=1 after translating origin to (1,0): replace x=X+1, y=Y: (X+1)^2+$Y^2$=1, i.e., X^{2+2X+Y}^2=0.

To find what a curve looks like in the new system, substitute the FORWARD transformation: X=... and Y=... expressions for x,y.