A hyperbola is the set of all points in theplane in which the difference of the distancesfrom two distinct fixed points is constant. The foci is the constant, that if F1 and F2 arethe foci of the hyperbola and P and Q are anytwo points on the hyperbola. Foci Formula: |PF₁ – PF₂ |= |QF₁ – QF₂ |
Center- the midpoint of the line segmentwhose endpoints are the foci. Formula for center: F₁F₂/2 Vertex- the point on each branch of thehyperbola that is nearest to the center.
Asymptotes- The lines that the curveapproaches as it recedes from the center. Asyou move further out along the branches, thedistance between points on the hyperbolaand the asymptotes approaches zero. Transverse axis- the line segment connectingthe vertices. Also has a length of 2a units. Conjugate axis- the segment perpendicularto the transverse axis through the center.Also has a length of 2b units.
For a hyperbola the relationship among a, b,and c is represented by a2 + b2 =c2. Theasymptotes contain the diagonals of therectangle which the diagonals meet coincideswith the center of the hyperbola. C > a for the hyperbola. For standard for of a hyperbola with it’sorigin as its center can be derived from thefoci are on the x- axis at (c,0) and (-c,0) andthe coordinates of any point on the hyperbolaare (x,
Distance formula: |√((x + c)2 + y2 )- √((x +c)2 + y2 )= |c + a – (c –a)| Hyperbola Formula: |PF2 –PF1 | = |VF2 – VF1| If the foci are on the y-axis, the equation isy2/a2 – x2 /b2 = 1 The standard form of the equation of thehyperbola with center other than the origin isa translation of the parent graph to a centerat (h, k).