Rotation of Axes; General Form of a Conic

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Presentation transcript:

Rotation of Axes; General Form of a Conic

Identifying Conics Except for degenerate cases: Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 Defines a parabola if B2 – 4AC = 0 Defines an ellipse (or a circle) if B2 – 4AC < 0 Defines a hyperbola if B2 – 4AC > 0

1. Identify the graph of each equation without completing the square (Similar to p.417 #11-20, 43-52)

2. Identify the graph of each equation without completing the square (Similar to p.417 #11-20, 43-52)

3. Determine the appropriate rotation formulas to use so that the new equation contains no xy-term (Similar to p.417 #21-30)

Rotation Formulas

Standard Form of a Parabola

Standard Form of a Ellipse (a>b)

Standard Form of a Hyperbola

4. Rotate the axes so that the new equation contains no xy-term 4. Rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation (Similar to p.418 #31-42)

5. Rotate the axes so that the new equation contains no xy-term 5. Rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation (Similar to p.418 #31-42)

6. Rotate the axes so that the new equation contains no xy-term 6. Rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation (Similar to p.418 #31-42)