Question

To find the standard equation for a circle centered at the origin, we use the distance formula, since the radius measures? A. The distance from any point in the circle to the origin.B. The circumference c. The distance from any point inside the circle to the origin.D. The distance from the x-coordinate to the origin.

Answer 1

Answer:

  A. The distance from any point in the circle to the origin

Step-by-step explanation:

The distance formula tells you that the distance (d) is related to the coordinates of two points (x1, y1) and (x2, y2) by ...

  d² = (x2 -x1)² +(y2 -y1)²

For points (x, y) on the circle and (0, 0) at the origin, this becomes ...

  d² = (x -0)² +(y -0)²

If we want the distance to the point (x, y) to be equal to the radius of the circle, this becomes ...

  x² +y² = r² . . . . . . the standard equation of a circle centered at the origin