Question

Complete the equation of this ˚le:

(x - [?])^2 + (y - [?])^2 = [?]
a) (x - 5)^2 + (y - 8)^2 = 64
b) (x + 5)^2 + (y + 8)^2 = 64
c) (x - 5)^2 + (y + 8)^2 = 64
d) (x + 5)^2 + (y - 8)^2 = 64

Answer 1

The equation (x - [?])^2 + (y - [?])^2 = [?] represents a circle in standard form. The correct equation is (x - 5)^2 + (y - 8)^2 = 64, with the center of the circle at (5, 8) and a radius of 8.

Step-by-step explanation:

The question asks to complete the equation of a circle in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. The equation (x - [?])^2 + (y - [?])^2 = [?] represents a circle in standard form. The values inside the brackets represent the coordinates of the center of the circle, and the value outside the brackets represents the square of the radius. To complete the equation, we need to determine the center and radius of the circle. Comparing the given options, we can see that option a) (x - 5)^2 + (y - 8)^2 = 64 has the correct form with the center of the circle at (5, 8) and a radius of 8.