Translation of axes

In mathematics, a translation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x'y'-Cartesian coordinate system in which the x' axis is parallel to the x axis and k units away, and the y' axis is parallel to the y axis and h units away. This means that the origin O' of the new coordinate system has coordinates (h, k) in the original system. The positive x' and y' directions are taken to be the same as the positive x and y directions. A point P has coordinates (x, y) with respect to the original system and coordinates (x', y') with respect to the new system, where x = x ′ + h {displaystyle x=x'+h}      and      y = y ′ + k {displaystyle y=y'+k}     (1) x ′ = x − h {displaystyle x'=x-h}      and      y ′ = y − k . {displaystyle y'=y-k.}     (2) A x 2 + C y 2 + D x + E y + F = 0 {displaystyle Ax^{2}+Cy^{2}+Dx+Ey+F=0}      ( A {displaystyle A} and C {displaystyle C} not both zero);    (3) 9 x ′ 2 + 25 y ′ 2 = 225. {displaystyle 9x'^{2}+25y'^{2}=225.}     (4) x ′ = x − h , y ′ = y − k , z ′ = z − l {displaystyle x'=x-h,qquad y'=y-k,qquad z'=z-l}     (5) A x 2 + B y 2 + C z 2 + D x y + E x z + F y z + G x + H y + K z + L = 0 , {displaystyle Ax^{2}+By^{2}+Cz^{2}+Dxy+Exz+Fyz+Gx+Hy+Kz+L=0,}     (6) In mathematics, a translation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x'y'-Cartesian coordinate system in which the x' axis is parallel to the x axis and k units away, and the y' axis is parallel to the y axis and h units away. This means that the origin O' of the new coordinate system has coordinates (h, k) in the original system. The positive x' and y' directions are taken to be the same as the positive x and y directions. A point P has coordinates (x, y) with respect to the original system and coordinates (x', y') with respect to the new system, where