Question

write the equation of this circle in standard form.

Explanation:

Step1: Identify the center of the circle

The center of the circle (h, k) is at (5, 0) as seen from the graph (the yellow dot is at x = 5, y = 0).

Step2: Determine the radius

The radius is the distance from the center (5, 0) to a point on the circle, e.g., (10, 0). Using the distance formula \( r=\vert10 - 5\vert= 5\) (or we can see from the graph the horizontal distance from center at x=5 to x=10 is 5 units).

Step3: Write the standard form of the circle's equation

The standard form of a circle's equation is \((x - h)^2+(y - k)^2=r^2\), where (h, k) is the center and r is the radius. Substituting h = 5, k = 0, and r = 5, we get \((x - 5)^2+(y - 0)^2=5^2\), which simplifies to \((x - 5)^2+y^2 = 25\).

Answer:

\((x - 5)^2+y^2 = 25\)