Common Core HSG.GPE.A.1 worksheet

Question 1

Find the centre of the circle x² + y² + 4x + 4y + 4 = 0. Type it like (2, −1).

Answer 

Question 2

A circle has centre (4, −5) and passes through (−4, −3). Its equation is (x − 4)² + (y + 5)² = k. Find k.

Answer 

Question 3

The circle x² + y² = r² passes through (−3, 4). What is r?

Answer 

Question 4

Where is the point (−2, 0) relative to the circle (x + 1)² + (y − 5)² = 100?

• A. Inside the circle
• B. On the circle
• C. Outside the circle

Question 5

Which is the equation of the circle with centre (4, −6) and radius 4?

• A. (x + 4)² + (y − 6)² = 4
• B. (x − 4)² + (y + 6)² = 4
• C. (x − 4)² + (y + 6)² = 16
• D. (x + 4)² + (y − 6)² = 16

Question 6

Find the radius of the circle x² + y² + 2x − 2y − 34 = 0.

Answer 

Question 7

What is the centre of the circle (x + 5)² + (y + 2)² = 16? Type it like (2, −1).

Answer 

Question 8

Find the centre of the circle x² + y² − 2x − 10y + 17 = 0. Type it like (2, −1).

Answer 

Question 9

A circle has centre (−3, 4) and passes through (−1, −3). Its equation is (x + 3)² + (y − 4)² = k. Find k.

Answer 

Question 10

The circle x² + y² = r² passes through (−8, 6). What is r?

Answer 

Question 11

Where is the point (−7, −3) relative to the circle (x − 1)² + (y + 3)² = 49?

• A. Inside the circle
• B. On the circle
• C. Outside the circle

Question 12

Which is the equation of the circle with centre (6, 3) and radius 6?

• A. (x − 3)² + (y − 6)² = 36
• B. (x − 6)² + (y − 3)² = 6
• C. (x − 6)² + (y − 3)² = 36
• D. (x + 6)² + (y + 3)² = 6

Question 13

Find the radius of the circle x² + y² − 8x + 12y − 12 = 0.

Answer 

Question 14

What is the centre of the circle x² + (y + 4)² = 25? Type it like (2, −1).

Answer 

Question 15

Find the centre of the circle x² + y² + 4x + 10y − 20 = 0. Type it like (2, −1).

Answer 

Question 16

A circle has centre (−4, −3) and passes through (6, 2). Its equation is (x + 4)² + (y + 3)² = k. Find k.

Answer