Geometry of Circles: Equations from Center and Points

What are the components needed to write the equation of a circle?

• Circumference and area

• Radius and diameter

• Center and a point on the circle

• Pi and radius

What does the 'h' and 'k' represent in the circle's equation?

• Coordinates of the circle's center

• Slope and intercept

• Coordinates of a point on the circle

• Radius and diameter

What is the first step in finding the equation of a circle given its center and a point on it?

• Calculate the diameter

• Identify the center and the point

• Find the circumference

• Determine the radius squared

How do you calculate the radius squared in the equation of a circle?

• Use the distance formula between the center and a point on the circle

• Subtract the center from the given point

• Multiply the coordinates of the center

• Add the center to the given point

If the center of a circle is (-2, -1) and a point on the circle is (4, 1), what is R squared?

• 36

• 40

• 38

• 42

What is the standard form equation of a circle?

• (x - h)^2 + (y - k)^2 = r^2

• x^2 + y^2 = r^2

• (x + h)^2 + (y + k)^2 = r

• x^2 + y^2 = d^2

How do you transform the equation when the center has negative coordinates?

• Add the coordinates directly

• Change subtraction to addition for negative values

• Subtract the absolute values of the coordinates

• Multiply the coordinates by -1

After finding R squared, what is the next step in deriving the circle's equation?

• Insert R squared back into the equation

• Calculate the circumference

• Calculate the circle's area

• Find the circle's diameter

For a circle with center (1, -1) and a point (-3, 4) on it, what is the value of R squared?

• 39

• 41

• 40

• 42

In the second example, what are the coordinates of the center?

• (4, 1)

• (-3, 4)

• (1, -1)

• (-2, -1)