Which is the standard equation for a circle centered at the origin with radius r?A.x2 + y2 = r2B.x2 + y2 = rC.x2 = y2 + r2D.x + y = rSUBMITarrow_backPREVIOUS

Break Down the Problem

1. Identify the characteristics of the circle: centered at the origin and having a radius $r$.
2. Recall the standard form of the equation for a circle in a Cartesian coordinate system.

Relevant Concepts

The standard equation for a circle in a Cartesian plane is based on the definition of a circle, which is the set of all points that are a fixed distance (the radius) from a center point. The standard formula is given by: $(x - h)^2 + (y - k)^2 = r^2$ where $(h, k)$ is the center of the circle and $r$ is the radius.

Analysis and Detail

Since the circle is centered at the origin $(0, 0)$, the equation simplifies to: $(x - 0)^2 + (y - 0)^2 = r^2$ This simplifies further to: $x^2 + y^2 = r^2$

Verify and Summarize

• We have identified and derived the standard equation for a circle centered at the origin, confirming that the form $x^2 + y^2 = r^2$ corresponds correctly to our initial conditions.

Final Answer

The standard equation for a circle centered at the origin with radius $r$ is: A. $x^2 + y^2 = r^2$