Question

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)

Answer 1

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

Answer 2

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`