Question

The center of a circle is (3, -7) and a point on the circle is (0,0).

Find the radius of the circle.
Write the standard equation of the circle.
Graph the circle.

Answer 1

Explanation:

If (0, 0) is on the circle and the center is at (3, -7), then the radius is the distance from (0, 0) to (3, -7), which (according to the Pythagorean Theorem) is r = √(3² + [-7]²) = √(9 + 49) = √58 = r. Thus, r² = 58.

Adapting the standard equation of a circle (x - a)² + (y - b)² = r², we get:

(x - 3)² + (y + 7)² = 58

To graph this, plot the center (3, -7). Setting a compass so that its points are r = √58 units apart, place one point on the center and draw a circle around this center.