Exploring the Equation of Circles

What is the center of a circle if the equation is (x - 3)^2 + (y + 4)^2 = 16?

• (3, 4)

• (-3, 4)

• (-3, -4)

• (3, -4)

What is the radius of a circle if its equation is x^2 + y^2 = 49?

• 343

• 49

• 14

• 7

If the equation of a circle is (x - 5)^2 + (y + 5)^2 = 64, what is the radius?

• 32

• 64

• 8

• 16

If the radius squared of a circle is 25, what is the radius?

• 25

• 5

• 625

• 50

What is the center of the circle if the equation is (x + 4)^2 + (y - 3)^2 = 36?

• (-4, -3)

• (4, 3)

• (4, -3)

• (-4, 3)

How do you write the equation of a circle with center at (1, -3) and radius 2?

• (x - 1)^2 + (y + 3)^2 = 2

• (x + 1)^2 + (y - 3)^2 = 4

• (x + 1)^2 + (y - 3)^2 = 2

• (x - 1)^2 + (y + 3)^2 = 4

Which equation represents a circle with center at (-2, 5) and radius 3?

• (x + 2)^2 + (y - 5)^2 = 9

• (x - 2)^2 + (y + 5)^2 = 9

• (x - 2)^2 + (y + 5)^2 = 3

• (x + 2)^2 + (y - 5)^2 = 3

What is the correct equation for a circle with center at (0, -2) and radius 3?

• x^2 + (y + 2)^2 = 9

• (x + 2)^2 + y^2 = 9

• x^2 + (y - 2)^2 = 9

• (x - 2)^2 + y^2 = 9

If a point is located at (2, 3) and the circle's center is at (2, 1), what is the distance between the point and the center?

• 3

• 2

• 1

• 4

How do you determine if a point (x, y) is inside a circle with a given radius?

• Subtract the radius from the coordinates of the point

• Calculate the distance from the point to the center and compare it to the radius

• Multiply the coordinates of the point by the radius

• Add the coordinates of the point and compare to the radius