A circle is drawn on the Cartesian coordinate system with axes labeled x and y, both ranging from -5 to 5. The point at the topmost part of the circle farthest from the center is at coordinates $\left(0,2\right)$(0,2). The point at the bottommost part of the circle farthest from the center is at coordinates $\left(0,-2\right)$(0,−2). The point at the leftmost part of the circle farthest from the center is at coordinates $\left(-2,0\right)$(−2,0). The point at the rightmost part of the circle farthest from the center is at coordinates $\left(2,0\right)$(2,0). The coordinates are not explicitly labeled in the image.

State the coordinates of the center in the form $\left(a,b\right)$(a,b).

State the radius.

Easy

< 1min

Consider the graph of the circle shown below.

Easy

< 1min

Consider the circle in the graph.

Easy

< 1min

The equation of a circle is given by $x^2+y^2=32$x2+y2=32

Easy

1min

Outcomes

MA.912.GR.3.2

Given a mathematical context, use coordinate geometry to classify or justify definitions, properties and theorems involving circles, triangles or quadrilaterals.

MA.912.GR.3.3

Use coordinate geometry to solve mathematical and real-world geometric problems involving lines, circles, triangles and quadrilaterals.

MA.912.GR.7.2

Given a mathematical or real-world context, derive and create the equation of a circle using key features.

MA.912.GR.7.3

Graph and solve mathematical and real-world problems that are modeled with an equation of a circle. Determine and interpret key features in terms of the context.

10.06 Equations of circles

Interactive practice questions

Outcomes

MA.912.GR.3.2

MA.912.GR.3.3

MA.912.GR.7.2

MA.912.GR.7.3

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