Answer to Question #145010 in Analytic Geometry for Sarita bartwal

Question

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

Answer 1

$(x-2)^2 = y(y-1)^2$

Let the point on the curve with respect to old axis is (x,y)

Let the same point on the curve with respect to new axis be (x ′ ,y ′ )

The new co-ordinates are shifted by (2,1) Thus x=x ′ +2 and y=y ′ +1

Replacing the value of x and y in $(x-2)^2 = y(y-1)^2$ ,we get

$(x'+2-2)^2 = (y'+1)(y'+1-1)^2\\ (x')^2 = (y'+1)(y')^2$

answer: $(x')^2 = (y'+1)(y')^2$