Question

what is the equation of the circle if the radius is 6 and the center is (4, -7)?
○ (x + 4)² + (y - 7)² = 6
○ (x - 4)² + (y + 7)² = 6
○ (x + 4)² + (y - 7)² = 36
○ (x - 4)² + (y + 7)² = 36

Explanation:

Step1: Recall circle equation formula

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

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

Given center \((4, -7)\), so \(h = 4\), \(k = -7\), and radius \(r = 6\). Then \(r^2 = 6^2 = 36\).

Step3: Substitute into the formula

Substitute \(h = 4\), \(k = -7\), and \(r^2 = 36\) into \((x - h)^2 + (y - k)^2 = r^2\). We get \((x - 4)^2 + (y - (-7))^2 = 36\), which simplifies to \((x - 4)^2 + (y + 7)^2 = 36\).

Answer:

D. \((x - 4)^2 + (y + 7)^2 = 36\) (assuming the last option is D, with the equation \((x - 4)^2 + (y + 7)^2 = 36\))