Question

Find the new equation of the curve `(x-2)^2=y(y-1)^2` by transforming to parallel axes through the point `(2, 1)`?

Answer 1

New equation is `(x-4)^2=(y-1)(y-2)^2`

Explanation:

Transforming to parallel axes through `(x_1,y_1)` means the transformation `x->x+x_1` and `y->y+y_1`

Hence here it is `x->x+2` and `y->y+1`

and equation `(x-2)^2=y(y-1)^2`

becomes `(x+2-2)^2=(y+1)(y+1-1)^2`

or `x^2=y^2(y+1)`

The graph of given equation `(x-2)^2=y(y-1)^2` appears as

graph{((x-2)^2-y(y-1)^2)(x-2)(y-1)=0 [-10, 10, -5, 5]}

and graph of given equation `x^2=y^2(y+1)` appears as

graph{x^2=y^2(y+1) [-10, 10, -5, 5]}