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Question 5 (12 points)

Graph the circle (x + 1)2 + (y - 3)2 = 16. Then find the distance from the center of the circle to each point below.
a. (2,1)
b. (4,1)
C. (3,3)

User Karthick Selvaraj
by
2.6k points

2 Answers

27 votes
27 votes

Compare with (x-h)^2+(y-k)^2=r^2

  • Centre=(h,k)=(-1,3)
  • r=4

Distance to (2,1)

  • √(2+1)^2+(1-3)^2=√13

Distance to (4,1)

  • √(4+1)^2+(1-3)^2=√29

Distance to (3,3)

  • √(3+1)^2+(3-3)^2=4
Question 5 (12 points) Graph the circle (x + 1)2 + (y - 3)2 = 16. Then find the distance-example-1
User Anurag Rana
by
3.5k points
22 votes
22 votes

Answer:

see attached for diagram

a) √13

b) √29

c) 4

Explanation:

Equation of the circle:
(x + 1)^2 + (y - 3)^2 = 16

⇒ center = (-1, 3)

⇒ radius = √16 = 4

Distance between 2 points formula:


√((x_2-x_1)^2+(y_2-y_1)^2)

a) let (-1, 3) =
(x_1,y_1)

let (2, 1) =
(x_2, y_2)


\implies √((2+1)^2+(1-3)^2) =√(13)

b) let (-1, 3) =
(x_1,y_1)

let (4, 1) =
(x_2, y_2)


\implies √((4+1)^2+(1-3)^2) =√(29)

c) let (-1, 3) =
(x_1,y_1)

let (3, 3) =
(x_2, y_2)


\implies √((3+1)^2+(3-3)^2) =4

Question 5 (12 points) Graph the circle (x + 1)2 + (y - 3)2 = 16. Then find the distance-example-1
User Bajaj
by
2.9k points