Question

2 select the correct answer. the equation ((x - 1)^2 + (y + 1)^2 = r^2) represents circle j. the point (d(0, 3)) lies on the circle. what is (r), the length of the radius of circle j?
a. 17
b. 5
c. (sqrt{17})
d. (sqrt{5})

Explanation:

Step1: Substitute point D into the circle equation

Since point \( D(0, 3) \) lies on the circle \( (x - 1)^2+(y + 1)^2=r^2 \), we substitute \( x = 0 \) and \( y = 3 \) into the equation.
\[
(0 - 1)^2+(3 + 1)^2=r^2
\]

Step2: Simplify the left - hand side

First, calculate \( (0 - 1)^2=(- 1)^2 = 1 \), and \( (3 + 1)^2=4^2=16 \). Then add these two results together:
\[
1 + 16=r^2
\]
\[
r^2=17
\]

Step3: Solve for r

Since \( r \) represents the radius of a circle, \( r>0 \). Taking the square root of both sides of \( r^2 = 17 \), we get \( r=\sqrt{17} \) (we discard the negative root because the radius is a non - negative quantity).

Answer:

C. \( \sqrt{17} \)