General Form: Left-Right Opening Hyperbola: Vertical Axis of Symmetry: where If , square hyperbola Horizontal Axis of Symmetry: (h, k) = vertex of hyperbola Center: Vertices: Alternate Form: Foci: relative to center (h,k) Focus length, c, from center: Up-Down Opening Hyperbola: Hyperbola Eccentricity: p = semi-latus rectum Alternate Form: 3-D or the line segment running from the focus to the curve in the directions Interesting Note: The difference between the distances General Form: If B ≠ 0, then coordinate system: from each focus to a point on the curve is constant. where A and D have different signs New = (x’, y’), Old = (x, y) rotates through angle from x-axis Limit 1st Hint: Use Product Rule for Unit tangent vector Derivative Unit normal vector 2nd Derivative
Hyperbola General Form: where If , square hyperbola Center: Vertices: Foci: Focus length, c, from center: Eccentricity: 3-D If B ≠ 0, then coordinate system: New = (x’, y’), Old = (x, y) rotates through angle from x-axis Vertical Axis of Symmetry: Horizontal Axis of Symmetry: relative to center (h,k) p = semi-latus rectum or the line segment running from the focus to the curve in the directions Interesting Note: The difference between the distances from each focus to a point on the curve is constant. Left-Right Opening Hyperbola: (h, k) = vertex of hyperbola Alternate Form: Up-Down Opening Hyperbola: Alternate Form: General Form: where A and D have different signs Limit 1st Derivative Hint: Use Product Rule for Unit tangent vector 2nd Derivative Unit normal vector
Harolds_Calculus_3_Cheat_Sheet_2017.docx