QuestionCircle A's equation is $(x-3)^{2}+(y+1)^{2}=16$ . What is the equation of circle B after translating A right by 2 units?

Studdy Solution

STEP 1

Assumptions1. Circle A has equation $(x-3)^{}+(y+1)^{}=16$ . Circle B is obtained by translating circle A to the right by units3. The translation does not change the radius of the circle

STEP 2

The general equation of a circle in the xy-plane is given by $(x-h)^2 + (y-k)^2 = r^2$ , where $(h,k)$ is the center of the circle and $r$ is the radius.

STEP 3

From the equation of circle A, we can see that the center of circle A is at $(3,-1)$ and the radius is $\sqrt{16}=$ .

STEP 4

To obtain circle B, we translate circle A to the right by2 units. This means we add2 to the x-coordinate of the center of circle A.

STEP 5

Calculate the x-coordinate of the center of circle B.
$h_B = h_A +2$

STEP 6

Plug in the values for $h_A$ and2 to calculate $h_B$ .
$h_B =3 +2$

STEP 7

Calculate the x-coordinate of the center of circle B.
$h_B =3 +2 =5$

STEP 8

The y-coordinate of the center of circle B is the same as that of circle A, because we only translated the circle to the right. So, $k_B = k_A = -1$ .

STEP 9

The radius of circle B is the same as that of circle A, because the translation does not change the radius. So, $r_B = r_A =4$ .

STEP 10

Now we can write the equation of circle B using the values of $h_B$ , $k_B$ , and $r_B$ .
$(x-h_B)^2 + (y-k_B)^2 = r_B^2$

STEP 11

Plug in the values for $h_B$ , $k_B$ , and $r_B$ to write the equation of circle B.
(x-5)^ + (y+)^ =4^

STEP 12

implify the equation of circle B.
$(x-5)^2 + (y+)^2 =16$ The equation of circle B is $(x-5)^2 + (y+)^2 =16$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms