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?

(-4,3)  , r = 5

Step-by-step 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

option 1 is correct.

step-by-step explanation:

y varies inversely with x and constant of variation is 4

the equation will be:

y = k/x

where k =4 so,

y = 4/x

if we put values of x of option 1 in the above equation and find values of y

y = 4/-2 => y =-2

y = 4/-1 => y = -4

y = 4/1 => y = 4

y = 4/2 => y =2

so, all the values of x and y are correct.

if we put values of x given in other options and find value of y we cannot find whole table satisfying the equation.

hence option 1 is correct.