Question

write the standard form of the equation of the circle with radius r and center (h, k). 13) r = 12; (h, k) = (6, 7) a) (x + 6)^2 + (y + 7)^2 = 144 b) (x + 6)^2 + (y + 7)^2 = 12 c) (x - 6)^2 + (y - 7)^2 = 12 d) (x - 6)^2 + (y - 7)^2 = 144

Explanation:

Step1: Recall circle - equation formula

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

Step2: Substitute given values

Given \(h = 6\), \(k = 7\), and \(r = 12\). Substitute these values into the formula: \((x - 6)^2+(y - 7)^2=12^2\).

Step3: Calculate \(r^2\)

Since \(r = 12\), \(r^2=144\). So the equation is \((x - 6)^2+(y - 7)^2=144\).

Answer:

D. \((x - 6)^2+(y - 7)^2=144\)