Circles and parabolas

The equation of a circle in both forms, and a parabola read both ways — built from its focus and directrix, then read back off the equation.

4 sheets · 32 questions · one answer key · 5 pages

Recommended for grades 9–10

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Circles in standard form Sheet 1 of 4

The equation of a circleFrom the standard form

Name: Date:

Write the center and radius of each circle.

1(x + 2)² + (y + 4)² = 9

2(x − 6)² + (y + 3)² = 81

3(x + 5)² + (y + 3)² = 81

4(x + 4)² + y² = 4

5x² + (y − 4)² = 81

6(x − 2)² + (y − 4)² = 81

7x² + (y + 2)² = 36

8(x − 6)² + y² = 9

The equation of a circleBy completing the square

Name: Date:

Complete the square to find the center and radius of each circle.

1x² + y² − 4x − 96 = 0

2x² + y² − 2x − 8 = 0

3x² + y² − 6x = 0

4x² + y² + 2x − 80 = 0

5x² + y² − 10x − 6y + 25 = 0

6x² + y² − 12x − 2y − 12 = 0

7x² + y² − 10x + 8y + 25 = 0

8x² + y² + 2x − 10y + = 0

The equation of a parabolaFrom the focus and directrix

Name: Date:

Write the equation of each parabola from its focus and directrix.

1focus (−1, 5)directrix y = −1

2focus (2, −3)directrix y = 3

3focus (2, 5)directrix y = 3

4focus (4, 0)directrix y = −8

5focus (−1, −6)directrix y = 2

6focus (−2, −5)directrix y = −3

7focus (−4, −1)directrix y = −3

8focus (1, 1)directrix y = 5

The equation of a parabolaBack to the focus and directrix

Name: Date:

Find the focus and the directrix of each parabola.

1(x + 2)² = −4(y − 3)

2x² = 16(y + 3)

3(x + 3)² = 8(y − 4)

4(x − 4)² = 8(y − 4)

5(x − 2)² = 12(y + 4)

6(x + 4)² = −8(y − 2)

7x² = −4(y − 3)

8(x − 4)² = −12(y − 3)

Power Pack · Circles and parabolasAnswer key

Circles in standard form

1. (x + 2)² + (y + 4)² = 9 → center (−2, −4), radius 32. (x − 6)² + (y + 3)² = 81 → center (6, −3), radius 93. (x + 5)² + (y + 3)² = 81 → center (−5, −3), radius 94. (x + 4)² + y² = 4 → center (−4, 0), radius 25. x² + (y − 4)² = 81 → center (0, 4), radius 96. (x − 2)² + (y − 4)² = 81 → center (2, 4), radius 97. x² + (y + 2)² = 36 → center (0, −2), radius 68. (x − 6)² + y² = 9 → center (6, 0), radius 3

Circles in general form

1. x² + y² − 4x − 96 = 0 → center (2, 0), radius 102. x² + y² − 2x − 8 = 0 → center (1, 0), radius 33. x² + y² − 6x = 0 → center (3, 0), radius 34. x² + y² + 2x − 80 = 0 → center (−1, 0), radius 95. x² + y² − 10x − 6y + 25 = 0 → center (5, 3), radius 36. x² + y² − 12x − 2y − 12 = 0 → center (6, 1), radius 77. x² + y² − 10x + 8y + 25 = 0 → center (5, −4), radius 48. x² + y² + 2x − 10y + = 0 → center (−1, 5), radius 5

Write the parabola

1. focus (−1, 5), y = −1 → (x + 1)² = 12(y − 2)2. focus (2, −3), y = 3 → (x − 2)² = −12y3. focus (2, 5), y = 3 → (x − 2)² = 4(y − 4)4. focus (4, 0), y = −8 → (x − 4)² = 16(y + 4)5. focus (−1, −6), y = 2 → (x + 1)² = −16(y + 2)6. focus (−2, −5), y = −3 → (x + 2)² = −4(y + 4)7. focus (−4, −1), y = −3 → (x + 4)² = 4(y + 2)8. focus (1, 1), y = 5 → (x − 1)² = −8(y − 3)

Read the focus and directrix

1. (x + 2)² = −4(y − 3) → focus (−2, 2), directrix y = 42. x² = 16(y + 3) → focus (0, 1), directrix y = −73. (x + 3)² = 8(y − 4) → focus (−3, 6), directrix y = 24. (x − 4)² = 8(y − 4) → focus (4, 6), directrix y = 25. (x − 2)² = 12(y + 4) → focus (2, −1), directrix y = −76. (x + 4)² = −8(y − 2) → focus (−4, 0), directrix y = 47. x² = −4(y − 3) → focus (0, 2), directrix y = 48. (x − 4)² = −12(y − 3) → focus (4, 0), directrix y = 6

Circles and parabolas

What is in the pack

The algebra track

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