Algebra 2 Ch. 9 Vocab & Formulas
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15 terms
Terms | Definitions |
|---|---|
 Distance Formula | d = square root of (x2 - x1)^2 + (y2 - y1)^2 |
| Midpoint Formula | M[(x1 + x2) / 2, (y1 + y2) / 2] |
| Circle definition | A circle is the set of all points in a plane that are equidistant from a fixed point. |
| Circle Formula | (x-h)^2 + (y-k)^2 = r^2 |
| Parabola definition | A parabola is the set of all points in a plane equidistant from a given point and a given line. |
| Focus/directrix eqaution for parabola | a = (1/4p) (find p) |
| Parabola equation | opens up/down: y - k = (1 / 4p)(x - h)^2 opens left/right: x - h = (1 / 4p)(x - h)^2 p = distance from vertex to focus |
| Ellipse definition | An ellipse is the set of all point in a plane such that the sum of the distance to two fixed points is a constant. |
| Ellipse equation | horizontal: [(x - h)^2 / a^2] + [(y - k)^2 / b^2] = 1 Vertical: [(x - h)^2 / b^2] + [(y - k)^2 / a^2] = 1 a^2 - b^2 = c^2 |
| Hyperbola definition | A hyperbola is the set of all points in a plane such that the difference to two fixed points is a constant. |
| Hyperbola equation | left/right: [(x - h)^2 / a^2] - [(y - k)^2 / b^2] = 1 Up/down: [(y - k)^2 / a^2] - [(x - h)^2 / b^2] = 1 |
| 1 quadratic | parabola |
| 2 quadratics w/ same sign & same coefficient | circle |
| 2 quadratics w/ same sign & different coefficients | ellipse |
| 2 quadratics w/ different signs | hyperbola |
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