Equations of Circles: Key Concepts and Applications

What is the standard form of a circle's equation?

• x^2 + y^2 + r^2 = 0

• (x - h)^2 + (y - k)^2 = r^2

• (x + h)^2 + (y + k)^2 = r^2

• x^2 + y^2 = r^2

In the equation of a circle, what do the variables h and k represent?

• The coordinates of the circle's center

• The circle's diameter

• The slope of the tangent to the circle

• The circle's radius

How do you find the radius of a circle from its equation?

• Multiply h and k

• Square root of r squared

• Square root of k

• Square root of h

If a circle's equation is (x - 3)^2 + (y + 4)^2 = 25, what is its center?

• (-3, -4)

• (3, 4)

• (-3, 4)

• (3, -4)

How do you graph a circle given its equation?

• Plot the center and draw a square around it

• Plot the center and radius on a coordinate plane

• Draw a circle and then find the center

• Plot the center and draw a circle with the radius

What does the radius squared equal in the circle's equation?

• h + k

• The diameter

• The area of the circle

• r squared

How do you find the center of a circle from its equation?

• The opposite of h and k values

• The sum of h and k

• The product of h and k

• The square root of r squared

What is the radius of a circle with an equation of (x + 2)^2 + (y - 5)^2 = 36?

• 12

• 6

• 18

• 36

If a circle is translated left 6 units and up 7 units, what happens to its center?

• It moves 7 units left and 6 units up

• It stays the same

• It moves 6 units left and 7 units up

• It moves 6 units right and 7 units down

How do you convert a circle's diameter to its radius for use in the equation?

• Multiply by 2

• Take the square root

• Divide by 2

• Square it