Set: Calculus: Conic Sections

Familiarize

Learn

Test

Play Scatter

Play Space Race
Combine with other sets Login to add to Favorites
Print: Term List | Flashcards Editing not allowed
Export Deleting not allowed

Share these flash cards

With group: None
HTML link to set: Plain link:
Share on Facebook Share on MySpace

All 19 Terms

Term Definition
parabola with a vertical axis (x - h)² = 4p(y - k), vertex: (h,k) directrix: y = k - p, focus: (h, k+p), axis: x = h
parabola with a horizontal axis (y - h)² = 4p(x - k), vertex: (h,k) directrix: y = x - h, focus: ( k+p, h), axis: y = h
reflective property of a parabola The tangent line to the parabola at point P makes equal angles with the following two lines. 1. The line passing through P and the focus. 2. The line passing through P parallel to the axis of the parabola
focal chord a line segment that passes through the focus of a parabola and has endpoints on the parabola
latus rectum the specific focal chord perpendicular to the axis of the parabola
ellipse with a horizontal major axis (x - h)²/a² + (y - k)²/b² = 1 center: (h,k), vertices: (h ±a, k), Foci: (h±c, k), c² = a² - b²
ellipse with a vertical major axis (x - h)²/b² + (y - k)²/a² = 1 center: (h,k), vertices: (h, k ±a), Foci: (h, k±c), c² = a² - b²
reflective property of an ellipse The tangent line to the ellipse at point P makes equal angles with the lines through P and the foci.
eccentricity e = c/a
hyperbola with a horizontal transverse axis (x - h)²/a² - (y - k)²/b² = 1 center: (h,k), vertices: (h ±a, k), Foci: (h±c, k), b² = c² - a²
hyperbola with a vertical transverse axis (y - h)²/a² - (x - k)²/b² = 1 center: (h,k), vertices: (h, k ±a), Foci: (h, k±c), b² = c² - a²
asymptotes of a hyperbola with a horizontal transverse axis y = k + (b/a)(x -h) and y = k - (b/a)(x -h)
asymptotes of a hyperbola with a vertical transverse axis y = k + (a/b)(x -h) and y = k - (a/b)(x -h)
general conic equation Ax² + Bxy + Cy² + Dx + Ey + F = 0
rotation of axis x = x' cosθ - y'sinθ, y = x'sinθ + y'cosθ, where cot 2θ = (A - C)/B and B' =0
rotation invariants 1. F = F', 2. A + C = A' + C',3. B² - 4AC = (B')² - 4A'C'
ellipse or circle discriminant B² - 4AC < 0
parabola discriminant B² - 4AC = 0
hyperbola discriminant B² - 4AC > 0

Set Information

Terms 19
Creator jtwilliams00
Created October 26, 2008
Groups None
Subjects mathematics, calculus, conics, conic
Access Anyone
Edit Creator Only
Pop out

Discuss

No Messages
Last Message: never

You must be logged in to discuss this set.

Top Users

  1. jtwilliams00 - 12 scores

Most Missed Words

  1. parabola with a vertical axis → (x - h)² = 4p(y - k), vertex: (h,k) directrix: y = k - p, focus: (h, k+p), axis: x = h - 2 misses
  2. focal chord → a line segment that passes through the focus of a parabola and has endpoints on the parabola - 1 miss
  3. hyperbola with a horizontal transverse axis → (x - h)²/a² - (y - k)²/b² = 1 center: (h,k), vertices: (h ±a, k), Foci: (h±c, k), b² = c² - a² - 1 miss
  4. hyperbola with a vertical transverse axis → (y - h)²/a² - (x - k)²/b² = 1 center: (h,k), vertices: (h, k ±a), Foci: (h, k±c), b² = c² - a² - 1 miss
  5. eccentricity → e = c/a - 1 miss
  6. parabola with a horizontal axis → (y - h)² = 4p(x - k), vertex: (h,k) directrix: y = x - h, focus: ( k+p, h), axis: y = h - 1 miss
  7. latus rectum → the specific focal chord perpendicular to the axis of the parabola - 1 miss