Question

write the standard equation of the circle with the given center and radius.
a. center (5, - 8), radius 6
\\((x - h)^2 + (y - k)^2 = r^2\\)
b. center (0, 12) and radius 2.5
what is the equation of this circle?
\\((x + 8)^2 + (y - 5)^2 = 36\\)
\\((x + 8)^2 + (y - 5)^2 = 6\\)
\\((x - 5)^2 + (y + 8)^2 = 36\\)
\\((x - 5)^2 + (y - 8)^2 = 36\\)
rewatch

Explanation:

Step1: Recall circle's standard equation

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

Step2: Substitute center \((5, -8)\) and \(r = 6\)

Here, \(h = 5\), \(k = -8\), \(r = 6\). Substitute into the formula: \((x - 5)^2 + (y - (-8))^2 = 6^2\), which simplifies to \((x - 5)^2 + (y + 8)^2 = 36\).

Answer:

\((x - 5)^2 + (y + 8)^2 = 36\) (corresponding to the option: \((x - 5)^2 + (y + 8)^2 = 36\))