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10.8 Circles on Coordinate Plane

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Equations of Circles
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Any point with coordinates that satisfy this Standard Equation exists ON the circle. However, it is possible to determine if a point exists INSIDE the circle or OUTSIDE the circle as well!

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Now let's work backwards and go from center and radius to an equation or from the graph to the equation.

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1.

The GEOMETRY Final will be on FORMATIVE! You MUST bring your fully charged, school provided Chromebook in order to take your final.

Mark "TRUE" if you read and understand this.

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2.

Determine the length of side BC in the diagram

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3.

Inscribed Angles Review

Solve the following problem.

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4.

Consider a circle with radius=10 units and center C(0,0). Point A(6, 8) and Point Q(-8, -6) exist on the circle.

Draw the radius to Point A.

Draw the vertical line segment \overline{AB} to the x-axis.

Draw the horizontal line segment \overline{BC} to the y-axis.

You have just created right triangle \triangle ABC. Repeat these steps to create right triangle \triangle QPC.

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5.

Use the Pythagorean Theorem to relate the three side lengths of the right triangles.

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6.

The coordinates from A(6,8) satisfy the Pythagorean Theorem:

The coordinates from Q(-8,-6), although they are negative, also satisfy the Pythagorean Theorem:

With this information in mind, what Standard Equation can you write to represent the equation of a circle with center (0,0) and radius r?

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7.

What is the radius of the circle in each equation?

Draggable itemarrow_right_altCorresponding Item

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8.

Transform the Unit Circle according to the given equation. Graph the circle on the coordinate plane.

Equation:

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9.

Describe the circle given by the equation

radius:

center:

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10.

Write the equation for a circle with center (0, −4) and radius 8.

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11.

Write the equation for the circle shown below.

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12.

A circle has a diameter with endpoints at (6, 5) and (8, 5).

Write the equation for the circle.

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13.

Graph the circle and type the center and radius in the Show Your Work box.

Center:

Radius:

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14.

Graph the circle and type the center and radius in the corresponding boxes.

Center:

Radius:

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15.

Identify each part of the circle given its equations. Then, graph the circle.

Center:

Radius:

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16.

Identify each part of the circle given its equations.

Center:

Radius:

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17.

Given the center and radius or diameter, write the equation in standard form.

Center: (5,3)

Radius: 2

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18.

Given the center and radius or diameter, write the equation in standard form.

Center: (-1,7)

Radius: 6

Finished with all greens?

Complete the "Writing Equations of Circles" exercise on Khan Academy.

--> be sure you have completed the Arc Length & Area of Sector exercises too

CIRCLES TEST in two class periods!