Circles in general form: complete the square and graph

Grade 10 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

1.
Milo writes the edge of a bike wheel as 2x² + 2y² − 8x + 12y − 6 = 0. Which equation is the circle in standard form?
- (x − 2)² + (y + 3)² = 4
- (x − 4)² + (y + 6)² = 58
- (x + 2)² + (y − 3)² = 16
- (x − 2)² + (y + 3)² = 16
2.
Noah writes the edge of a cake as 3x² + 3y² + 12x − 6y − 33 = 0. Which equation is the circle in standard form?
Use the picture in question 1.
- (x + 2)² + (y − 1)² = 4
- (x − 2)² + (y + 1)² = 16
- (x + 2)² + (y − 1)² = 16
- (x + 6)² + (y − 3)² = 78
3.
Ren writes the edge of a round flower bed as 2x² + 2y² + 4x + 16y + 2 = 0. Which equation is the circle in standard form?
Use the picture in question 1.
- (x + 1)² + (y + 4)² = 4
- (x + 2)² + (y + 8)² = 66
- (x + 1)² + (y + 4)² = 16
- (x − 1)² + (y − 4)² = 16
4.
Tala checks the equation x² + y² − 4x + 6y + 13 = 0 before drawing a clock face. What is its graph?
Use the picture in question 1.
- a circle with radius √26
- no graph at all
- a circle with radius 4
- a single point
5.
Zee checks the equation x² + y² + 2x − 4y + 9 = 0 before drawing a pizza. What is its graph?
Use the picture in question 1.
- a single point
- no graph at all
- a circle with radius 4
- a circle with radius √14
6.
Ari checks the equation x² + y² − 6x − 8y + 9 = 0 before drawing a pond. What is its graph?
Use the picture in question 1.
- a circle with radius 4
- a single point
- no graph at all
- a circle with radius √34
7.
Bo checks the equation x² + y² + 8x + 2y + 17 = 0 before drawing a drum top. What is its graph?
Use the picture in question 1.
- a circle with radius √34
- a circle with radius 4
- no graph at all
- a single point
Esme writes the edge of a bike wheel as x² + y² − 4x + 2y − 3 = 0. Give an exact answer, simplified. How long is the radius?
Use the picture in question 1.
Jun writes the edge of a cake as x² + y² + 6x − 6y − 2 = 0. Give an exact answer, simplified. How long is the radius?
Use the picture in question 1.
Kira writes the edge of a sun in a mural as x² + y² − 2x − 10y + 8 = 0. Give an exact answer, simplified. How long is the radius?
Use the picture in question 1.

Circles in general form: complete the square and graph

Answer Key - Grade 10 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1.
Milo writes the edge of a bike wheel as 2x² + 2y² − 8x + 12y − 6 = 0. Which equation is the circle in standard form?
- (x − 2)² + (y + 3)² = 4
- (x − 4)² + (y + 6)² = 58
- (x + 2)² + (y − 3)² = 16
- (x − 2)² + (y + 3)² = 16
2.
Noah writes the edge of a cake as 3x² + 3y² + 12x − 6y − 33 = 0. Which equation is the circle in standard form?
Use the picture in question 1.
- (x + 2)² + (y − 1)² = 4
- (x − 2)² + (y + 1)² = 16
- (x + 2)² + (y − 1)² = 16
- (x + 6)² + (y − 3)² = 78
3.
Ren writes the edge of a round flower bed as 2x² + 2y² + 4x + 16y + 2 = 0. Which equation is the circle in standard form?
Use the picture in question 1.
- (x + 1)² + (y + 4)² = 4
- (x + 2)² + (y + 8)² = 66
- (x + 1)² + (y + 4)² = 16
- (x − 1)² + (y − 4)² = 16
4.
Tala checks the equation x² + y² − 4x + 6y + 13 = 0 before drawing a clock face. What is its graph?
Use the picture in question 1.
- a circle with radius √26
- no graph at all
- a circle with radius 4
- a single point
5.
Zee checks the equation x² + y² + 2x − 4y + 9 = 0 before drawing a pizza. What is its graph?
Use the picture in question 1.
- a single point
- no graph at all
- a circle with radius 4
- a circle with radius √14
6.
Ari checks the equation x² + y² − 6x − 8y + 9 = 0 before drawing a pond. What is its graph?
Use the picture in question 1.
- a circle with radius 4
- a single point
- no graph at all
- a circle with radius √34
7.
Bo checks the equation x² + y² + 8x + 2y + 17 = 0 before drawing a drum top. What is its graph?
Use the picture in question 1.
- a circle with radius √34
- a circle with radius 4
- no graph at all
- a single point
Esme writes the edge of a bike wheel as x² + y² − 4x + 2y − 3 = 0. Give an exact answer, simplified. How long is the radius?
Use the picture in question 1.
2√2
Jun writes the edge of a cake as x² + y² + 6x − 6y − 2 = 0. Give an exact answer, simplified. How long is the radius?
Use the picture in question 1.
2√5
Kira writes the edge of a sun in a mural as x² + y² − 2x − 10y + 8 = 0. Give an exact answer, simplified. How long is the radius?
Use the picture in question 1.
3√2