Equations of Circles

What is the standard form of the equation of a circle?

• (x + h)^2 - (y + k)^2 = r^2

• (x - h)^2 + (y - k)^2 = r^2

• (x - h)^2 - (y - k)^2 = r^2

• (x + h)^2 + (y + k)^2 = r^2

How do you find the center and radius of a circle given its equation in standard form?

• Complete the square to rewrite the equation in the form (x - h)^2 + (y - k)^2 = r^2

• Guess the center and radius based on the coefficients of the equation

• Graph the equation and measure the center and radius using a ruler

• Use the quadratic formula to solve for the center and radius

If the equation of a circle is given as (x-3)^2 + (y+4)^2 = 25, what is the center and radius of the circle?

• (5, -3) and 7

• (3, -4) and 5

• (0, 0) and 10

• (2, 4) and 6

Write the equation of a circle with center (2, -5) and radius 7.

• (x - 2)^2 + (y - 5)^2 = 49

• (x - 2)^2 + (y + 5)^2 = 49

• (x - 2)^2 + (y + 5)^2 = 64

• (x + 2)^2 + (y - 5)^2 = 49

What is the equation of a circle with center (0, 0) and radius 6?

• x^2 + y^2 = 36

• 2x + 2y = 36

• x^2 + 6y = 0

• x^2 - y^2 = 36

If the equation of a circle is given as (x+1)^2 + (y-2)^2 = 36, what is the center and radius of the circle?

• (1, -2) and 36

• (-1, 2) and 12

• (-2, 1) and 6

• (-1, 2) and 6

How do you write the equation of a circle given its center and radius?

• (x + h)^2 + (y + k)^2 = r^2

• (x - h)^2 - (y - k)^2 = r^2

• (x + h)^2 - (y + k)^2 = r^2

• (x - h)^2 + (y - k)^2 = r^2

Find the center and radius of the circle with equation (x-5)^2 + (y+3)^2 = 49.

• Center: (8, -2), Radius: 6

• Center: (0, 0), Radius: 5

• Center: (5, 3), Radius: 10

• Center: (5, -3), Radius: 7

What is the equation of a circle with center (-4, 7) and radius 10?

• (x + 7)^2 + (y - 4)^2 = 100

• (x + 4)^2 + (y - 7)^2 = 100

• (x - 4)^2 + (y - 7)^2 = 10

• (x - 4)^2 + (y + 7)^2 = 100

If the equation of a circle is given as (x-2)^2 + (y+1)^2 = 16, what is the center and radius of the circle?

• (3, 2) and 5

• (0, 0) and 8

• (2, -3) and 6

• (2, -1) and 4