Equation of a Circle

Equation of a Circle

Learning Target: I can write the equation of a circle and graph a circle from it's equation.

Multiple Choice

What does the equation of a circle with center at (0,0) look like?

• $$y=x^2$$

• $$y=mx+b$$

• $$x^2+y^2=r^2$$

• $$y=a\left(x-h\right)^2+k$$

Equation of a circle with center at (0,0)

Multiple Choice

What is the equation for this circle?

• (x+1)+(y+1)=9
• x²+y²=9
• x+y=9

Multiple Choice

Write the equation at the origin with radius 6.  

• x^2 + y^2 = 6
• x^2 + y^2 = 36
• x  + y = 6
• x + y = 36

Multiple Choice

What is the center of the circle with equation x² + y² = 1?

• (1, 1)
• (0, 0)
• not enough information
• (-1, -1)

What if the center isn't (0,0)?
Equation of a circle

Open Ended

Why has there not been an h and k value in the equations we have looked at so far, like this one?

$$x^2+y^2=81$$  

Writing Equations of Circles

We can write equations of circles from their graphs.

Locate the center of the circle. This usually marked with a dot

Multiple Choice

What is the center of this circle? Which is the correct ordered pair?

• (2, 2)

• (2, -2)

• (0, 0)

• (-2, 2)

Writing Equations of Circles

The other piece of information we need is the radius.

You can calculate the radius by counting the number of units from the center to any point on the circle.

​r

Multiple Choice

What is the radius of this circle?

• 2

• 6

• 3

• 5

Writing Equations of Circles

Multiple Choice

What does "h" stand for in (h,k)?

• h is the radius of the circle

• h is the distance of the circle

• h is the y in the coordinate point

• h is the x in the coordinate point

Multiple Choice

What does the "k" in (h,k) stand for?

• k is the y coordinate point in the center of the circle

• k is the x coodinate point in the center of the circle

• k is the radius of the circle

• k is the distance of the circle

Multiple Choice

What does the r in the standard equation stand for?

• r is the distance of the circle

• r is the radius of the circle

• r is the x coordinate of the center of the circle

• r is the y coordinate of the center of the circle

Multiple Choice

What does (h,k) stand for in the standard circle equation?

• (h,k) is the center of the circle

• (h,k) is a point on the circle.

• (h,k) is a point that we guess and find

• (h,k) is the distance of the circle

Multiple Choice

Which is the standard form of the circle equation?

• $$\left(x-h\right)^2+\left(y-k\right)^2=r^2$$

• $$\left(x+h\right)^2+\left(y+k\right)^2=r^2$$

• $$\left(x-h\right)^2+\left(y-k\right)^2=r^{ }$$

• $$\left(x-h\right)^2-\left(y-k\right)^2=r^2$$

Multiple Choice

What is the equation of the circle?

• (x+1)^2 + (y +1)^2 = 3

• (x+1)^2 + (y -1)^2 = 3

• (x+1)^2 + (y +1)^2 = 9

• (x-1)^2 + (y -1)^2 = 9

Multiple Choice

What is the center and radius for a circle with the equation:
(x-4)²+(y+2)²=25

• C:(4, -2), r=5
• C:(-4, 2), r=5
• C:(4, -2), r=25
• C:(-4, 2), r=25

Multiple Choice

What is the radius of the circle
(x+7)²+(y-2)²=144?

• 7
• 12
• 13

Multiple Choice

Write the equation of a circle with center (7, 0) with radius 3. 

• (x - ^7)^2 + y^2 = 9
• x^2 + (y -7)^2 = 9
• (x - 7)^2 + y^2 = 3
• x^2 + (y -7)^2 = 3

Multiple Choice

Which graph corresponds to 
(x)²+ (y-6)²=9

• A
• B
• C
• D

Multiple Choice

In the equation (x-4)²+(x-3)²=25, the radius is

• 4
• 3
• 5
• 25

Multiple Choice

A line segment between two points on the circle which passes through the center

• Radius
• Diameter
• Chord
• Tangent

Multiple Choice

Circles with exactly the same radius measures are called

• Similar Circles
• Concentric Circles
• Congruent Circles
• Semicircle

Multiple Choice

Circles with exactly the same center are called

• Similar Circles
• Concentric Circles
• Congruent Circles
• Semicircle

Multiple Choice

The distance around a circle

• Diameter
• Radius
• Circumference
• Area

Multiple Choice

Write the equation of a circle with center
(7, 0) with radius 3. 

• (x - 7)² + y² = 9
• x² + (y -7)² = 9
• (x - 7)² + y² = 3
• x² + (y -7)² = 3

Multiple Choice

What is the center of the circle with this equation is (x+2)²+(y-4)²=41?

• (2,-5)
• (-2,4)
• (2,-4)
• (-2, -4)

Multiple Choice

What is the radius of the circle with this equation of  (x-5)²+(y+7)²=8?

• 4
• 8
• 4√2
• 2√2

Multiple Choice

Which choice is the equation of a circle with center (-3,4) and passing through (-6,0)?

• (x+3)²+(y-4)²=25

• (x+3)²+(y-4)²=27

• (x-3)²+(y+4)²=25

• (x-3)²+(y+4)²=27

Math Response

The diameter of a circle has length 14. The center is at (3, -2). Create the equation of the circle.

Type answer here

Correct Answer: \left(x-3\right)^2+\left(y+2\right)^2=49

Deg^°

Rad

Multiple Choice

The point (4,3) is on a circle whose center is at (1,3). Write the standard form of the equation of the circle.

• (x-3)²+(y-3)²=4

• (x+1)²+(y+3)²=9

• (x-1)²+(y-3)²=3

• (x-1)²+(y-3)²=9

Math Response

Write the equation of a circle with its diameter whose endpoints are (-5,-4) and (7,-4).

Hint: first find the center of the circle using midpoint formula.

Type answer here

Correct Answer: \left(x-1\right)^2+\left(y+4\right)^2=36

Deg^°

Rad

Draw

Graph $$\left(x-3\right)^2+\left(y+5\right)^2=\ 4^2$$