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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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