Algebra II - Conic Sections – Study Guide
I.
When working with conic sections, it is useful to know:
1) Distance formula d = √(x2 – x1)² + (y2 – y1)²
2) Midpoint formula mp =((x1 + x2) ÷ 2), ((y1 + y2) ÷ 2)
II.
Know the general formulas:
General: Ax² + Cy² + Dx + Ey + F = 0 (A, B, and C cannot all = 0)
Circle: x² + y² + Dx + Ey + F = 0 (x and y squared and equal coefficients)
Parabola: Ax² + Dx + Ey + F = 0 or Cy² + Dx + Ey + F = 0 (x or y squared)
Ellipse: Ax² - Cy² + Dx + Ey + F = 0 (same as general formula)
Hyperbola: Ax² + Cy² + Dx + Ey + F = 0 (x and y coefficients are opposites)
III. Circles: Equation of a circle  r² = (x-h)² + (y-k)²
Given center and radius, be able to determine equation.
Given center and radius, be able to determine equation.
Given center and endpoints of diameter, be able to determine equation.
Given equation, be able to sketch a circle.
Given graph, be able to determine equation.
IV.
Parabolas :
if x² 
If y² 
y-k = a(x-h)² or 4p(y-k) = (x-h)²
F (h, k + (1/4a)) axis: x = h
D: y = k – (1/4a)
x-h = a(y-k)² or 4p(x-h) = (y-k)²
F (h + (1/4a), k) axis: y = k
D: h = k – (1/4a)
Given the equation, be able to determine and sketch focus, directrix, and vertex.
Given focus and directrix, focus and vertex, directrix and vertex, and/or sketch,
determine equation.
Be able to explain how/why a parabola is a locus of points.
V.
Ellipsi:
((x-h)² ÷ a²) + ((y-k) ² ÷ b²) = 1
a² - b² = c² Foci (±c, k) or (h, ±c)
a>b
Know and use the following terms: major and minor axis, eccentricity, and co-vertices.
Know the meaning of and be able to use a, b and c.
Given the equation, be able to determine and sketch foci, vertices, and co-vertices.
Given foci, vertices, and co-vertices, and/or sketch, determine equation.
VI.
Hyperbolae:
or
((x-h)² ÷ a²) - ((y-k) ² ÷ b²) = 1
((y-k)² ÷ a²) - ((x-h) ² ÷ b²) = 1
a² + b² = c²
Know how to find/create fundamental rectangle, asymptotes, transverse, conjugate, and
sketch. Given transverse and conjugate, determine equation and sketch.
Algebra II - Unit VII - Conic Sections
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3/6/2016