Q.Obtain the new equation of the locus y² − 4x − 4y + 12 = 0 if the origin is shifted to the point O'(2, 2), the direction of axes remaining the same.

Shift of origin is the technique of sliding the coordinate axes to a new origin O′(h,k), keeping the new axes parallel to the old ones, so that a point's coordinates change from the old pair (x,y) to a new pair (x′,y′) related by x = x′+h and y = y′+k. This is useful because many equations become much simpler when written relative to a well-chosen new origin — a technique that shows up repeatedly in coordinate geometry to strip away linear terms and reveal an equation's underlying shape. Given the shift point and one set of coordinates, the formulas let you compute the other set directly by substitution. Given an equation of a curve in the old coordinates, substi …