Writing Circle Equations Without Knowing the Radius

What is required to write the equation of a circle?

• The area of the circle

• Just the circumference

• The center and the radius

• Only the diameter

How is the center of a circle represented in its equation?

• As the square root of the radius

• In the form (h, k) where h and k are subtracted from x and y respectively

• As the exponent of r

• As the coefficient of x and y

What does the equation (x - h)^2 + (y - k)^2 = r^2 represent?

• The diameter of a circle

• The circumference of a circle

• The equation of a circle with center (h, k) and radius r

• The area of a circle

How can the radius of a circle be found using two points?

• By calculating the slope between the points

• Through the Pythagorean theorem

• By adding the distances of the points from the origin

• Using the midpoint formula

What is the equation of a circle with a center at (3, -4) and a radius found using the Pythagorean theorem?

• x^2 + y^2 = 85

• (x - 3)^2 + (y + 4)^2 = 85

• (x + 3)^2 + (y - 4)^2 = 85

• x^2 + y^2 = r^2

How do you solve for the radius given the area of a circle?

• Multiply the area by π

• Divide the area by π and then square root

• Square root the area and then multiply by π

• Divide the area by 2π

What is the equation of a circle with a center at (-5, 2) and an area that leads to r^2 = 3?

• (x + 5)^2 + (y - 2)^2 = 3

• (x - 5)^2 + (y - 2)^2 = 3

• (x - 5)^2 + (y + 2)^2 = 3

• x^2 + y^2 = 3

What formula is used to find the radius from the circumference?

• C = πr^2

• C = 2πr

• C = πd

• C = 2r

What is the radius of a circle if its circumference is 10π?

• 10

• 5

• 2π

• 20π

What is the equation of a circle with a center at (0, 3) and a radius of 5?

• (x + 0)^2 + (y + 3)^2 = 25

• (x - 0)^2 + (y - 3)^2 = 25

• x^2 + y^2 = 5

• x^2 + (y - 3)^2 = 25