What are the coordinates of a point that lies on a circle centered at the origin with a radius of 5 units?

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The equation of a circle centered at the origin (0, 0) with a radius of 5 units is given by:

x² + y² = r²

Here, r represents the radius of the circle. In this case, the radius is 5, so we substitute it into the equation:

x² + y² = 5²

This simplifies to:

x² + y² = 25

Any point (x, y) that satisfies this equation lies on the circle. For example:

  • If x = 5, then y = 0. So, the point (5, 0) is on the circle.
  • If x = 0, then y = 5. Thus, the point (0, 5) is also on the circle.
  • If x = 3, we can find y using the equation: 3² + y² = 25 which gives y² = 16 or y = ±4. So, the points (3, 4) and (3, -4) are both on the circle.
  • Another possibility is if y = 5, you can find x: x² + 5² = 25, which leads to x² = 0, giving x = 0. This returns us to the point (0, 5).

In essence, there are infinitely many points that can be on this circle; you just need to select values for x or y and solve for the other coordinate using the equation x² + y² = 25.

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