Question

select the correct answer. which equation represents a circle with a center at (-5,5) and a radius of 3 units?
a. ((x + 5)^2 + (y - 5)^2 = 6)
b. ((x - 5)^2 + (y + 5)^2 = 3)
c. ((x - 5)^2 + (y - 5)^2 = 9)
d. ((x + 5)^2 + (y - 5)^2 = 3)
e. ((x + 5)^2 + (y - 5)^2 = 9)

Explanation:

Step1: Recall the circle equation formula

The standard form of a circle's equation is \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius.

Step2: Identify \(h\), \(k\), and \(r\)

Given center \((-5, 5)\), so \(h = -5\), \(k = 5\), and radius \(r = 3\).

Step3: Substitute into the formula

Substitute \(h = -5\), \(k = 5\), \(r = 3\) into \((x - h)^2 + (y - k)^2 = r^2\). We get \((x - (-5))^2 + (y - 5)^2 = 3^2\), which simplifies to \((x + 5)^2 + (y - 5)^2 = 9\).

Answer:

E. \((x + 5)^2 + (y - 5)^2 = 9\)