Question

1. what is the standard form of the equation of the circle in the graph? graph of a circle on a coordinate plane with grid, center at (1, 0) (visually estimated from the red dot) and radius 3 (visually estimated from the blue circles extent)

Explanation:

Step1: Identify the center of the circle

The center of the circle (h, k) is at (1, 0) as seen from the graph (the red dot is at x = 1, y = 0).

Step2: Determine the radius

The radius r is the distance from the center to the edge of the circle. Looking at the graph, the radius is 3 units (from x = 1 to x = 4 or x = -2, so the distance is 3).

Step3: Use the standard form of a circle's equation

The standard form of a circle's equation is \((x - h)^2 + (y - k)^2 = r^2\). Substituting h = 1, k = 0, and r = 3:
\((x - 1)^2 + (y - 0)^2 = 3^2\)
Simplify to get \((x - 1)^2 + y^2 = 9\).

Answer:

\((x - 1)^2 + y^2 = 9\)