Circle Equation Skills

What is the center of a circle with equation (x-3)^2 + (y+4)^2 = 25?

• (3, 4)

• (3, -1)

• (0, -4)

• (3, -4)

Calculate the radius of a circle with equation (x+2)^2 + (y-1)^2 = 36.

• 6

• 10

• 8

• 4

Write the standard form equation of a circle with center at (-1,5) and radius 7.

• (x + 1)^2 + (y + 5)^2 = 49

• (x - 1)^2 + (y - 5)^2 = 7

• (x + 1)^2 + (y - 5)^2 = 49

• (x - 1)^2 + (y + 5)^2 = 49

How does the radius of a circle affect the equation in standard form?

• The radius affects the equation by determining the value of r^2 in the standard form equation of a circle.

• The radius affects the equation by determining the value of pi in the standard form equation of a circle.

• The radius affects the equation by determining the value of the diameter in the standard form equation of a circle.

• The radius affects the equation by determining the value of the circumference in the standard form equation of a circle.

Graph the circle with equation (x-1)^2 + (y+3)^2 = 16 on the coordinate axes.

• The circle is centered at (2, -2) with a radius of 3.

• The circle is centered at (0, 0) with a radius of 5.

• The circle with equation (x-1)^2 + (y+3)^2 = 16 is centered at (1, -3) with a radius of 4.

• The circle is centered at (-1, 3) with a radius of 6.

Identify the center of the circle given the equation (x+5)^2 + (y-2)^2 = 49.

• (5, -2)

• (0, 0)

• (-5, 2)

• (3, 4)

If the radius of a circle is 10, what is the equation in standard form if the center is at (3,-4)?

• (x - 3)^2 + (y - 4)^2 = 100

• (x - 3)^2 + (y + 4)^2 = 10

• (x - 3)^2 + (y + 4)^2 = 100

• (x + 3)^2 + (y - 4)^2 = 100

Explain the relationship between the radius and the equation of a circle.

• The equation of a circle does not involve the radius

• The radius is a key component in the equation of a circle as it determines the size of the circle and its position relative to the center.

• The radius is only relevant for squares, not circles

• The radius has no impact on the equation of a circle

Determine the radius of a circle with equation (x-4)^2 + (y+1)^2 = 64.

• 8

• 6

• 10

• 4

What is the center of a circle with equation x^2 + y^2 = 36?

• (0, 0)

• (4, 4)

• (3, 3)

• (6, 6)