Answer to Question #271562 in Analytic Geometry for Talha

Question

Find the equation of the circle(x - 5)² + (y + 3)² = 25  translated through a vector

(-2,-2). Also Sketch it.

Answer 1

A translation vector is a type of transformation that moves a figure in the coordinate plane from one location to another. In other words, a translation vector can be thought of as a slide with no rotating. The slide won’t change the shape or size of the figure, and with no rotation, the orientation won’t change either.

Then after the translation through a vector $(-2,-2)$ we will have the new circle with the center $(5-2, -3-2)$ and radius $5$

$$(x-3)^2+(y+5)^2=25$$