Conics Formulas
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27 terms
Terms | Definitions |
|---|---|
 midpoint | (x₁ + x₂/2, y₁ + y₂/2) |
| distance | d = √(x₂ - x₁)² + (y₂ - y₁)² |
| parabola y = | y = a(x - h)² + k |
| parabola x = | x = a(y - k)² + h |
| parabola vertex | (h,k) |
| parabola axis of symmetry | x = h and y = k |
| parabola focus y | (h, k + 1/4a) |
| parabola focus x | (h + 1/4a, k) |
| parabola directrix y = | y = k - 1/4a |
| parabola directrix x = | x = h - 1/4a |
| parabola direction of opening y = | up if a > 0 down if a < 0 |
| parabola direction of opening x = | right if a > 0 left if a < 0 |
| parabola length of latus rectum | absolute value of 1/a |
| circle | (x - h)² + (y - k)² = r² |
| circle center | (h,k) |
| ellipse x | (x - h)²/a² + (y - k)²/b² = 1 |
| ellipse y | (y - k)²/a² + (x - h)²/b² = 1 |
| ellipse direction of major axis | x horizontal y vertical |
| ellipse foci x | (h ± c, k) |
| ellipse foci y | (h, k ± c) |
| ellipse abc | c² = a² - b² |
| hyperbola abc | c² = a² + b² |
| hyperbola x | (x - h)²/a² - (y - k)²/b² = 1 |
| hyperbola y | (y - k)²/a² - (x - h)²/b² = 1 |
| hyperbola direction of transverse axis x | horizontal |
| hyperbola direction of transverse axis y | vertical |
| hyperbola equations of asymptotes | y - k = ± b/a(x - h) |
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