Question

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 the point into the equation

The standard form of a circle's equation is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center. Here \(h = 1,k=-1\), and the point \((x,y)=(0,3)\). Substitute into \((x - 1)^2+(y + 1)^2=r^2\), we get \((0 - 1)^2+(3 + 1)^2=r^2\).

Step2: Calculate the left - hand side

First, \((0 - 1)^2=(-1)^2 = 1\), and \((3 + 1)^2=4^2=16\). Then \(1+16=r^2\), so \(r^2=17\). Since \(r>0\), \(r=\sqrt{17}\).

Answer:

C. \(\sqrt{17}\)