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Alg 2 Chapter 10 Review

Standard Form: x²+y²=r²
Translation: (x-h)²+(y-k)²=r²
Center: Opposite of (h,k)
Radius: Square root of r²
Standard Form: y=x²
Translation: y=(x-h)²+k
Vertex: (h,k)
Focus: Vertical-(h, k+c) Horizontal-(h+c,k)
Directrix: Vertical-y=k-c Horizontal-x=h-c
A or C: a=1/4c
Vertical Hyperbola
Standard Form:y²/a²-x²/b²=1
Translation Form:(y-k)²/a²-(x-h)²/b²=1
Vertices:(0,+- a) ; (h, k+-a)
Foci: (0, +-c); (h, k+-c)
Asymptotes: y-k=+-a/b*(x-h)
A,B,C Relationship:c²=a²+b²
Horizontal Hyperbola
Standard Form:x²/a²-y²/b²=1
Translation Form:(y-k)²/a²-(x-h)²/b²=1
Vertices:(0,+- a) ; (h+-a, k)
Foci: (0, +-c); (h+-c,k)
Asymptotes: y-k=+-b/a*(x-h)
A,B,C Relationship:c²=a²+b²
Vertical Ellipse
Standard Form: (x-h)²/b² + (y-k)²/a²=1
Vertices:(0,+-a) or (h,k+-a)
Co-Vertices: (+-b,0) or ((h +-b, k)
Foci: (0,+-c) or (h, k+-c)
A,B,C Relationship: c²=a²-b²
Horizontal Ellipse
Standard Form: (x-h)²/a² + (y-k)²/b²=1
Vertices:(+-a,0) or (h,k+-a)
Co-Vertices: (0,+-b) or ((h +-b, k)
Foci: (+-c,0) or (h+-c,k)
A,B,C Relationship: c²=a²-b²