10.8 Circles on Coordinate Plane

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18 questions
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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.

1

Determine the length of side BC in the diagram

1

Inscribed Angles Review

Solve the following problem.

Equations of Circles
1

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.

1

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

1

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?

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!
1

What is the radius of the circle in each equation?

Draggable itemCorresponding Item
1

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

Equation:

4
Describe the circle given by the equation


radius: _______
center: _______
5

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

5

Write the equation for the circle shown below.

5

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

4
Graph the circle and type the center and radius in the Show Your Work box.

Center: _______
Radius: _______
4
Graph the circle and type the center and radius in the corresponding boxes.

Center: _______
Radius: _______
4
Identify each part of the circle given its equations. Then, graph the circle.

Center: _______
Radius: _______
4
Identify each part of the circle given its equations.

Center: _______
Radius: _______
Now let's work backwards and go from center and radius to an equation or from the graph to the equation.
1

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

Center: (5,3)
Radius: 2

1

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!