Question

Use the graph below to write the equation of the circle.

Answer 1

(x - 1)² + (y - 3)² = 9

Explanation:

Circles are defined as shapes where all points are equidistant from the center.

Parts of a Circle

To find the equation of the circle we need to define a few parts of a circle. Firstly, the center of a circle is the point in the exact middle. Every point on the circle is an equal distance from the center. Next, the radius is the distance from the center of a circle to a point on the circle.

Finding the Equation

The equation of a circle is written as:

• (x - h)² + (x - k)² = r²

In this equation, h is the x-coordinate of the center, k is the y-coordinate of the center, and r is the radius.

The center of the circle shown is (1, 3). We know that this is the center because all parts of the circle are 3 units away from the point (1, 3). This means that h = 1 and k = 3.

The radius is the distance from the center to the circle. So, we can count the distance from (1, 3) to any point on the circle, such as (4, 3). These points are 3 units away from each other, so r = 3.

Plug these values into the equation:

• (x - 1)² + (y - 3)² = 9

This gives the final equation of the circle.