Exploring Equations of Circles

What does the center of a circle represent in its equation?

• The coordinates where the circle crosses the x-axis

• The length of the radius

• The highest point on the circle

• The coordinates of the middle point of the circle

What is the significance of 'R' in the circle's equation?

• It is the circumference of the circle

• It denotes the radius of the circle

• It indicates the area of the circle

• It represents the diameter of the circle

How does the sign of the center coordinates affect the equation of a circle?

• A negative x-coordinate turns into a plus sign in the equation

• The signs of the coordinates have no effect on the equation

• A positive y-coordinate remains a minus sign in the equation

• Both coordinates being negative does not change the equation

What does a plus sign inside the equation of a circle indicate about the center's coordinates?

• Both coordinates are positive

• The x-coordinate is positive

• The y-coordinate is positive

• At least one of the coordinates is negative

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

• By squaring the value of R in the equation

• By taking the square root of the value on the right side of the equation

• By doubling the value of R in the equation

• By adding the values of H and K

What does the equation of a circle look like when the center is at (-4, 1) and the radius is 1?

• (x - 4)^2 + (y - 1)^2 = 1

• (x - 4)^2 + (y + 1)^2 = 1

• (x + 4)^2 + (y - 1)^2 = 1

• (x + 4)^2 + (y + 1)^2 = 1

If the center of a circle is at (5, -1) and the radius is 10, what is the correct equation?

• (x - 5)^2 + (y - 1)^2 = 100

• (x - 5)^2 + (y + 1)^2 = 100

• (x + 5)^2 + (y + 1)^2 = 10

• (x + 5)^2 + (y - 1)^2 = 100

What is the radius of a circle if the equation is (x - 3)^2 + (y + 4)^2 = 4?

• 8 units

• 2 units

• 4 units

• 16 units

If a circle's equation is (x + 14)^2 + (y - 10)^2 = 4, what are the coordinates of its center?

• (14, -10)

• (-14, 10)

• (14, 10)

• (-14, -10)

How do you determine the center and radius of a circle from its equation?

• By using the coefficients of x and y for the center and the constant term for the radius

• By calculating the midpoint of H and K for the center and R for the radius

• By finding the maximum value of x and y for the center and the minimum value for the radius

• By identifying H and K for the center and square rooting R for the radius