EQUATIONS OF CIRCLES WORKSHEET FOR SAT

Problem 1 :

A circle in he xy-plane is centered at (1, 2) and contains the point (4, 6). Which of the following could be the equation of the circle ?

a) (x - 1)² + (y - 2)² = 5           b) (x - 1)² + (y - 2)² = 25

c) (x + 1)² + (y + 2)² = 5          d) (x + 1)² + (y + 2)² = 25

Solution

Problem 2 :

Which of the following is an equation of a circle in the xy-plane with center (3, -1) and a radius of 4 ?

a) (x - 3)² + (y + 1)² = 4      b) (x - 3)² + (y + 1)² = 16

c)  (x + 1)² + (y - 3)² = 4      d) (x + 3)² + (y - 1)² = 16

Solution

Problem 3 :

(x + 6)² + (y - 4)² = 100

The equation above defines a circle in the xy-plane. The circle intercepts the y-axis at (0, 12) and (0, c). What is the value of c ?

Solution

Problem 4 :

Which of the following is an equation of a circle in the xy-plane with center (2, -3) and a circumference of 20 π.

a) (x + 2)² + (y - 3)² = 20      b) (x - 2)² + (y + 3)² = 20

c)  (x - 2)² + (y + 3)² = 100      d) (x + 2)² + (y - 3)² = 400

Solution

Problem 5 :

x² + (y - 3)² = 25

The graph of the equation above in the xy-plane is a circle. At what points does the circle intersect the y-axis ?

a) (0, -2) and (0, 8)        b) (0, -3) and (0, 7)

c)  (0, -8) and (0, 2)        d)  (0, -22) and (0, 28)

Solution

Problem 6 :

x² - 4x + y² + 6y = 12

The graph of the equation in the xy-plane is a circle. What is the circumference of the circle ?

a)  5π     b)  10π     c)  25π      d)  50π

Solution

Problem 7 :

A circle in the xy-plane passes through the point (2, 2) and has a radius of 5. Which of the following could be an equation of the circle ?

a) (x - 1)² + y²  = 5            b) (x + 2)² + (y - 5)²  = 25

c) (x - 2)² + (y - 2)²  = 25       d) (x - 7)² + (y - 7)²  = 25

Solution