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12. Conic Sections
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Geometry

12.03 Manipulating circle equations

Lesson
Practice

Interactive practice questions

Consider the circle in the graph.

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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.
a

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

b

State the radius.

Easy
< 1min

Consider the graph of the circle shown below.

Easy
< 1min

Consider the circle in the graph.

Easy
< 1min

Consider the graph of the circle shown below.

Easy
< 1min
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Outcomes

GEO-G.GPE.1a

Derive the equation of a circle of given center and radius using the Pythagorean Theorem. Find the center and radius of a circle, given the equation of the circle.

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