Question

Suppose we apply the translation map Tv to each point on the circle (x + 4)^2 + (y − 3)^2 = 25.

a. What is the radius and center of the original circle?
b. Show that the image points satisfy the equation of another circle.
c. What are the center and radius of this image circle?

Answer 1

(-4,3) , r = 5

Explanation:

given,

equation of circle

(x + 4)² + (y − 3)²= 25.

general equation of the circle

(x - a)² + (y - b)² = r²

comparing the given equation from the general we get,

radius = r² = 25

r = 5

-a = 4 -b = -3

a = -4 b = 3

the center of the circle is (-4,3)

hence, all the specification is shown in the image attached below