Conic Sections Flashcards

Grade 11 · Math · Flashcards

Standard forms, key measurements, and properties of circles, parabolas, ellipses, and hyperbolas.

Flashcards

Circle: (x-h)² + (y-k)² = r²; all points equidistant from center (h,k)
Parabola opening up: x² = 4py; focus (0,p), directrix y=-p; vertex at origin
Parabola opening right: y² = 4px; focus (p,0), directrix x=-p; vertex at origin
Ellipse (horizontal major axis): x²/a² + y²/b² = 1, a > b; foci at (±c, 0), c² = a² - b²
Ellipse (vertical major axis): x²/b² + y²/a² = 1, a > b; foci at (0, ±c), c² = a² - b²
Hyperbola (horizontal): x²/a² - y²/b² = 1; foci at (±c, 0); c² = a² + b²
Hyperbola (vertical): y²/a² - x²/b² = 1; foci at (0, ±c); c² = a² + b²
Eccentricity formula: e = c/a; circle e=0, ellipse 0<e<1, parabola e=1, hyperbola e>1
Completing the square: Add (b/2)² to both sides to form a perfect square trinomial
Latus rectum: Chord through focus perpendicular to axis of symmetry; length = 4p for parabola, 2b²/a for ellipse
Discriminant test for conics: For Ax²+Bxy+Cy²+...: B²-4AC < 0 → ellipse/circle; = 0 → parabola; > 0 → hyperbola
Foci of ellipse: Located on major axis at distance c from center, where c = √(a²-b²)
Transverse axis: The axis of a hyperbola connecting its two vertices; length = 2a