10.8 Circles on Coordinate Plane

Required

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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

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Inscribed Angles Review

Solve the following problem.

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

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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!

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What is the radius of the circle in each equation?

Draggable item		Corresponding Item

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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.

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Write the equation for the circle shown below.

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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.

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

Center: (5,3)
Radius: 2

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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!

10.8 Circles on Coordinate Plane

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.

Determine the length of side BC in the diagram

Inscribed Angles ReviewSolve the following problem.

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

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?

What is the radius of the circle in each equation?

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

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

Write the equation for the circle shown below.

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

Given the center and radius or diameter, write the equation in standard form.Center: (5,3)Radius: 2

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!

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.

Determine the length of side BC in the diagram

Inscribed Angles ReviewSolve the following problem.

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

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?

What is the radius of the circle in each equation?

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

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

Write the equation for the circle shown below.

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

Given the center and radius or diameter, write the equation in standard form.Center: (5,3)Radius: 2

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!

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.

Inscribed Angles Review

Solve the following problem.

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?

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

Equation:

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

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

Center: (5,3)
Radius: 2

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

Center: (-1,7)
Radius: 6

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.

Inscribed Angles Review

Solve the following problem.

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?

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

Equation:

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

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

Center: (5,3)
Radius: 2

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

Center: (-1,7)
Radius: 6