Question

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

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

Step2: Calculate the left - hand side of the equation

First, calculate \((0 - 1)^2=(-1)^2 = 1\) and \((3 + 1)^2=4^2=16\).
Then \(1+16=r^2\), so \(r^2=17\).

Step3: Solve for \(r\)

Take the square root of both sides. Since \(r\) represents the radius (a non - negative quantity), \(r=\sqrt{17}\).

Answer:

C. \(\sqrt{17}\)