Question

what is the equation of the circle graphed below?
options:

• $x^2 + y^2 = 1$
• $x^2 + y^2 = 4$
• $x^2 + y^2 = 8$
• $x^2 + y^2 = 16$

Explanation:

Step1: Recall circle equation

The standard equation of a circle centered at the origin \((0,0)\) is \(x^{2}+y^{2}=r^{2}\), where \(r\) is the radius.

Step2: Determine radius from graph

From the graph, the circle extends 2 units from the origin (since it reaches from \(x = - 2\) to \(x = 2\) and \(y=-2\) to \(y = 2\)), so radius \(r = 2\).

Step3: Calculate \(r^{2}\)

\(r^{2}=2^{2}=4\). So the equation is \(x^{2}+y^{2}=4\).

Answer:

\(x^{2}+y^{2}=4\) (corresponding to the option \(x^{2}+y^{2}=4\))