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

Answer:

see attached for diagram

a) √13

b) √29

c) 4

Step-by-step explanation:

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

⇒ center = (-1, 3)

⇒ radius = √16 = 4

Distance between 2 points formula:

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

a)  let (-1, 3) = $(x_1,y_1)$

    let (2, 1) = $(x_2, y_2)$

 $\implies \sqrt{(2+1)^2+(1-3)^2} =\sqrt{13}$

b)  let (-1, 3) = $(x_1,y_1)$

    let (4, 1) = $(x_2, y_2)$

$\implies \sqrt{(4+1)^2+(1-3)^2} =\sqrt{29}$

c)  let (-1, 3) = $(x_1,y_1)$

    let (3, 3) = $(x_2, y_2)$

$\implies \sqrt{(3+1)^2+(3-3)^2} =4$

Answer 2

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