Deriving and using the equation of a circle

Which of the following equations of circles in standard form with center at (-5, -8) and a radius of 6 units?

• (x - 5)² - (y - 8)² = 36

• (x + 5)² - (y + 8)² = 36

• (x + 5)² - (y + 8)² = 36

• (x + 5)² + (y + 8)² = 36

What is the center and radius of this circle?
(x + 3)² + (y + 7)² = 4

• Center: (-3, -7)
   radius = 2
• Center: (3, 7)
   radius = 4
• Center: (-3, -7)
   radius = 4
• Center: (-3, 7)
   radius = 2

What equation do you get when you plug (12, -12) into the general form of the circle equation and simplify?

•  $12D+12E+F\ =\ -288$ 

•  $12D-12E+F=288$ 

•  $12D-12E+F=-288$ 

•  $-12D-12E+F=-288$ 

• A

• B

• C

• D

The point (-5,6) is on a circle with center (-1,3) write the equation of the circle (hint: remember distance between any point on the circle and the center is the radius length!)

• (x+1)² + (y-3)²= 4000

• (x+5)² + (y-0)²= 25

• (x+1)² + (y-3)²= 25

• (x-1)² + (y+3)²= 25

What is the equation of a circle with a center of (9, -2) and a diameter of 12

• (x-9)² + (y+2)² = 144

• (x+9)² + (y-2)² = 36

• (x-9)² + (y+2)² = 36

• (x+9)² + (y-2)² = 144

What is the equation of the circle, with centre (4,2) and radius 5 units?

• (x + 4)^2 + (y + 2)^2 = 25
• (x + 4)^2 + (y + 2)^2 = 5
• (x - 4)^2 + (y - 2)^2 = 5
• (x - 4)^2 + (y - 2)^2 = 25

In the equation for a circle, (x-h)²+(y-k)²= r², what part of the circle do the h, k and r represent?

• r is the hypotenuse, h and k are points on the circle

• r is the radius, h and k are points on the circle

• r is the roundness, h and k represent the center

• r is the radius, h and k represent the center

Is the point (3, -2) inside, outside or on a circle that is given by the equation:

(x+3)² + (y-2)² = 12

• inside

• on

• outside