[Music] chapter [Music] the same dire transform for [Music] [Music] [Music] vector vector fore [Music] fore fore spee [Music] speee [Music] fore for [Music] [Music] [Music] ex translation takes the origin then find the equation of the image for the circle whose equation is x + y for equation of x + y for for fore spe [Music] equation x² + y² = to 4 XE + 2 s + YC by the x + 2 2 + y - 2 X+ uh exercise 6.3 uh if translation T takes the origin minus then find the equation of the image for the circle whose equation is x² + y [Music] [Music] 16 of Circ [Music] fore fore speeech fore spee spee [Music] [Music] [Music] [Music] x x x X+ [Music] of the circle the image of uh the circle the circle given by given by x² + y = to 16 given [Music] is x + 3² + y - [Music] 3E fore for [Music] [Music] foree Circle [Music] x + y = y = equation the equation of the image will be the equation of the image x + 6 2 + y - 8 x + 4 cation x + 4² + y + 2 = 7 foreign [Music] spee - 2- 7 X foreign [Music] [Music] x + 4² + y + 2 [Music] s XE + XE + 7 + 4 y - 1 + 2 7 y + 1 [Music] = of the image will be the equation of uh uh Circle [Music] is x + 11 s + y + 1 [Music] = for- 4- [Music] 4 spee [Music] y 4AGE of [Music] the for [Music] [Music] [Music] X [Music] [Music] for x² + x² uh + y² [Music] 4 XE - 3² y Prime + 5 4E + [Music] 5 x - 6 XE +9 y prime plus y y Prime know y Prime + 25 25 - 4 y Prime - [Music] 20 XE s y Prime s - 6 x - 6 XE y Prime x² + y² - 6 x + 6 y - 7 = to [Music] [Music] Z foreign speee [Music]