Circles and their equations

What is the equation of a circle that has a center (0,0)?
where r = radius of the circle

• x²+y²=r²
• x²+y²=r
• x+y²=r²
• x²+y²=0

What is the equation of a circle that has a center (5,2)?
where r = 4

• (x-5)²+(y-4)²=3²
• (x-4)²+(y-5)²=3²
• (x-5)²+(y-2)²=4²
• (x)²+(y)²=4²

Tags

CCSS.HSG.GPE.A.1

What is the equation of a circle that has a center (-3,-5)?
where r = 7

• (x-3)²+(y-5)²=7²
• (x-5)²+(y-3)²=7²
• (x-5)²+(y-2)²=7²
• (x+3)²+(y+5)²=7²

If the circle touches the x axis (only one point of intersection:
The equation of a circle with centre at (h, k) and radius equal to a, is (x - h)² + (y - k)² = a² When the circle touches x-axis i.e., k = a.
Which of the following equations represent this?

• (x-3)²+(y-5)²= 3²
• (x-5)²+(y-3)²=5²
• (x)²+(y)²= 3²
• (x-5)²+(y-3)²= 3²

If the circle touches the y axis (only one point of intersection:
The equation of a circle with centre at (h, k) and radius equal to a, is (x - h)² + (y - k)² = a² When the circle touches x-axis i.e., h = a.
Which of the following equations represent this?

• (x-3)²+(y-5)²= 3²
• (x-5)²+(y-3)²=5²
• (x)²+(y)²= 3²
• (x-5)²+(y-3)²= 3²

What are the y intercepts of the circle
x²+y²=36
Hint substitute x =0 

• +6
• +5 and -5
• -6 and +6
• (0,0)

Does the point (4,5)  lie on the line 
(x+2)²+(y+2)²=81
Hint substitute x=4 and y=5 and see if the left side is equal the right side.

• yes
• No

Tags

CCSS.HSG.GPE.A.1

CCSS.HSA.REI.D.10

What are the x intercepts of the circle
x²+y²=25
Hint substitute y =0 

• +5
• +5 and -5
• -5
• (0,0)

Does the point (4,5)  lie on the line 
(x+2)²+(y+2)²=85
Hint substitute x=4 and y=5 and see if the left side is equal the right side.

• yes
• No

Determine whether the  point (5,-3) is on, inside, or outside the circle defined by x²+y²=34

• On
• Inside
• Outside
• Off the graph!