Classifying Conics Worksheets
Read standard-form conic equations to identify centers, vertices, dimensions and curve types.
Before you begin
Factor polynomials, use exponent laws and solve equations with domain restrictions.
Worked example
Classify the conic: (x + 1)² + (y - 3)² = 4.
- Equal positive squared coefficients: circle. Unequal positive squared coefficients: ellipse.
- Opposite signs on the squared terms: hyperbola. One squared variable: parabola.
Answer: Circle
Check your result using the method in the example before moving to the next question.
Choose your level
These sets use the same exercise types and number ranges across level labels. Choose a fresh set for additional practice.
- Easy: Start with the preview and follow the worked example.
- Medium: Practice the same exercise types with a fresh numbered set.
- Hard: Use another set to practice explaining and checking your answers.
Questions and answer calculations checked on 2026-09-17. How we check worksheets. Free for personal and classroom use.
Preview and print an easy set
Try six questions below, or choose a full set at your level.
1
Classify the conic: (x + 3)² + (y + 1)² = 9.
2
Classify the conic: (x - 2)²/5 + (y + 5)²/6 = 1.
3
Classify the conic: (x - 3)²/2 − (y - 1)²/3 = 1.
4
Classify the conic: y = 3(x - 2)² - 3.
5
Classify the conic: (x - 1)² + (y - 4)² = 4.
6
Classify the conic: (x - 5)²/5 + (y - 4)²/6 = 1.
Answer Key
1. Circle2. Ellipse3. Hyperbola4. Parabola5. Circle6. Ellipse