Question

A circle has a diameter starting at the point (-2, 0) and ending at (2,0). Explain how you would use this information to write the equation of the circle.

A) x^2 + y^2 = 4
B) (x + 2)^2 + y^2 = 4
C) (x - 2)^2 + y^2 = 4
D) x^2 + (y - 2)^2 = 4

Answer 1

The equation of a circle with diameter endpoints at (-2, 0) and (2, 0) is x^2 + y^2 = 4, based on the midpoint as the circle's center (0, 0) and radius of 2 units.

Step-by-step explanation:

To write the equation of a circle with a diameter that starts at (-2, 0) and ends at (2, 0), we need to remember that the standard form of a circle equation is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. In this case, since the diameter is along the x-axis and has endpoints at (-2, 0) and (2, 0), the center of the circle will be the midpoint between these two points, which is (0, 0). The length of the diameter is 4 units (from -2 to 2), so the radius r is half of that, which is 2 units. Therefore, the equation of the circle is x^2 + y^2 = 4.