When a basic form is translated by (p, q), replace x with x−p and y with y−q.
Example ① Convert x² + 4y² − 2x + 8y + 1 = 0 to standard form.
Solution:Completing the square: (x−1)² + 4(y+1)² = 4. Dividing both sides by 4:
(x−1)²/4 + (y+1)² = 1 (an ellipse centered at (1, −1))
Solution:Completing the square: (x−1)² + 4(y+1)² = 4. Dividing both sides by 4:
(x−1)²/4 + (y+1)² = 1 (an ellipse centered at (1, −1))
Key Point
- Complete the square to convert to standard form, then identify the features
Practice Problems
- What kind of figure is represented by x² + y² − 2x + 4y + 1 = 0?
Answers and Explanations
- Answer:A circle with center (1,−2) and radius 2