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Circle Equations and Properties

Circle Equations and Properties

Assessment

Interactive Video

•

Mathematics

•

9th - 10th Grade

•

Practice Problem

•

Hard

Created by

Thomas White

FREE Resource

This video tutorial by Mr. West covers graphing circles on a coordinate plane. It begins with an introduction to graphing circles and basic algebra concepts. The tutorial explains how to graph circles centered at the origin using the equation x^2 + y^2 = r^2, where r is the radius. It then moves on to graphing circles with centers not at the origin, using the equation (x-h)^2 + (y-k)^2 = r^2, where (h, k) is the center. The video includes example problems and solutions, demonstrating how to find equations for circles with given centers and radii. Finally, it shows how to graph circles from given equations, identifying the center and radius.

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26 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the main topic of the lesson introduced by Mr. West?

Graphing parabolas

Graphing ellipses

Graphing circles

Graphing lines

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the equation of a circle with its center at the origin?

x^2 + y^2 = 2r

x^2 + y^2 = r^2

x^2 + y^2 = r

x^2 + y^2 = 2r^2

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

If a circle has a radius of 4, what is the equation when centered at the origin?

x^2 + y^2 = 12

x^2 + y^2 = 16

x^2 + y^2 = 8

x^2 + y^2 = 4

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the equation of a circle with center (0, 0) and radius 5?

x^2 + y^2 = 20

x^2 + y^2 = 10

x^2 + y^2 = 25

x^2 + y^2 = 5

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What changes in the circle's equation when the center is not at the origin?

The equation becomes linear

The x and y terms are adjusted by h and k

The equation includes a tangent

The radius is squared

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the equation of a circle with center (3, -2) and radius 4?

(x + 3)^2 + (y - 2)^2 = 8

(x - 3)^2 + (y + 2)^2 = 16

(x + 3)^2 + (y - 2)^2 = 16

(x - 3)^2 + (y + 2)^2 = 8

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the equation of a circle with center (-3, 4) and radius 6?

(x - 3)^2 + (y + 4)^2 = 12

(x + 3)^2 + (y - 4)^2 = 12

(x - 3)^2 + (y + 4)^2 = 36

(x + 3)^2 + (y - 4)^2 = 36

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