Equations of Circles: Center at (0,0)

Deriving Equations of Circles

GEOM.12E Show that the equation of a circle with center at the origin and radius r is x2+ y2= r2and determine the
equation for the graph of a circle with radius r and center (h, k), (x – h)2+ (y – k)2= r2

Objectives

• LO: SWBAT Show that the equation of a circle with center at the

origin and radius r is x2+ y2= r2 and determine the equation for the
graph of a circle with radius r and center
(h, k), (x – h)2+ (y – k)2= r2.

• DOL: Given 5 problems, students will correctly show that the

equation of a circle with center at the origin and radius r is x2+ y2=
r2 and determine the equation for the graph of a circle with radius r
and center (h, k), (x – h)2+ (y – k)2= r2in at least 4 of 5
questions.

Vocabulary

Open Ended

A point equidistant from any point on the circle is called what?

Fill in the Blank

The distance from the center of the circle to any point on the circle is called the ______?

Drag and Drop

The diameter is also double the

Placeholder

Drag these tiles and drop them in the correct blank above

radius

circumference

area

volume

Equations of a circle

• Today we will learn about equations of circles. Recall that a circle is the set of points on a plane equidistant from a given point.

• We will learn how to create an equation of a circle using its center and its radius.

Equation of a circle w/ center (0,0)

Let's determine the lengths of the given right triangle.

•Horizontal Side Length:

•Vertical Side Length:

Using Pythagorean Theorem: c2 = a2 + b2

Substitute a ,b , & c with x ,y , & r

Drag and Drop

When a circle's center is at (0,0), what are the lengths of the sides of the right triangle?

Vertical Side Length: ​

Placeholder

Horizontal Side Length: ​

Placeholder

Drag these tiles and drop them in the correct blank above

y

x

Math Response

Write the equation of the circle with center at (0,0) and radius equal to 6.

Type answer here

Correct Answer: x^2+y^2=36

Deg^°

Rad

Math Response

Write the equation of the circle with center at (0,0) and radius equal to 12.

Type answer here

Correct Answer: x^2+y^2=144

Deg^°

Rad

Math Response

Determine the equation of the given circle.

Type answer here

Correct Answer: x^2+y^2=25

Deg^°

Rad

Labelling

Label each question with the correct comments of the circle's equation.

Drag labels to their correct position on the image

(0,0) for 4

r = 9

(0,0) for 3

Multiple Choice

The equation of a circle is $$x^2+y^2=4$$ , determine if point (-4, 1) lies on, in, or outside the circle.

• Lies IN the circle

• Lies ON the circle

• Lies OUTSIDE the circle

Multiple Choice

The equation of a circle is $$x^2+y^2=34$$ , determine if point (3, –5) lies on, in, or outside the circle.

• Lies IN the circle

• Lies ON the circle

• Lies OUTSIDE the circle

Skills Practice and DOL!!!!