Grade 10 · Math · Geometry

10th grade Circles in general form: complete the square and graph worksheet

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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 − 2)² + (y + 3)² = 16
- (x − 4)² + (y + 6)² = 58
- (x + 2)² + (y − 3)² = 16
2.
Pia writes the edge of a sun in a mural as 4x² + 4y² − 16x − 8y − 16 = 0. Which equation is the circle in standard form?
Use the picture in question 1.
- (x − 2)² + (y − 1)² = 3
- (x − 8)² + (y − 4)² = 96
- (x − 2)² + (y − 1)² = 9
- (x + 2)² + (y + 1)² = 9
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 = 16
- (x + 1)² + (y + 4)² = 16
- (x + 2)² + (y + 8)² = 66
- (x + 1)² + (y + 4)² = 4
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
- a single point
- no graph at all
- a circle with radius 4
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 circle with radius √14
- a circle with radius 4
- no graph at all
- a single point
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 √34
- a circle with radius 4
- no graph at all
- a single point
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
- no graph at all
- a single point
- a circle with radius 4
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.
Luz writes the edge of a round flower bed as x² + y² + 8x + 4y + 8 = 0. Give an exact answer, simplified. How long is the radius?
Use the picture in question 1.

10th grade Circles in general form: complete the square and graph worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Circles in general form. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can find the number that completes a square, and write the bracket it makes.
I can turn x² + y² + Dx + Ey + F = 0 into (x − h)² + (y − k)² = r² and read the center and radius.
I can tell when an equation is a circle, a single point, or no graph.

Standard: G-GPE.A.1

Words to know

general form: x² + y² + Dx + Ey + F = 0: everything multiplied out.

standard form: (x − h)² + (y − k)² = r²: center and radius show.

complete the square: Add (half the x-number)² to make a full square bracket.

constant: The number with no x or y (the F).

Common mistakes

Your child halved the number but did not square it.

Your child squared the whole number instead of half of it.

Your child flipped a sign when writing the bracket or the center.

What to say

Ask: how big is the missing corner square?

Ask: how many strips is the 6x split into?

Ask: does x² − 4x come from (x − 2)² or (x + 2)²?

Questions parents ask

What is the most common mistake with circles in general form: complete the square and graph?

Your child halved the number but did not square it.

How can I help my child with circles in general form: complete the square and graph?

Ask: how big is the missing corner square?

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More geometry

See all Geometry

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