Hyperbola Formulas

 

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Hyperbolas: Standard Form

Horizontal

"a" is the number in the denominator of the positive term

If the x-term is positive, then the hyperbola is horizontal

a = semi-transverse axis

b = semi-conjugate axis

center: (h, k)

vertices: (h + a, k), (h - a, k)

c = distance from the center to each focus along the transverse axis

foci: (h + c, k), (h - c, k)

The eccentricity e > 1

 

 

 

 

Vertical

"a" is the number in the denominator of the positive term

If the y-term is positive, then hyperbola is vertical

a = semi-transverse axis

b = semi-conjugate axis

center: (h, k)

vertices: (h, k + a), (h, k - a)

c = distance from the center to each focus along the transverse axis

foci: (h, k + c), (h, k - c)

 

The eccentricity e > 1

 

 

 

 

Ax˛ + By˛ + Cx + Dy + E = 0

1) A & B must have different signs (one positive and the other negative).

2) A & B must be different numbers or opposites (same number with different signs)

 

 

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