NOTE: We are going to use the section formula to derive the equation of hyperbola, as we did for ellipse. Since there are 2 variants of the formula (external and internal division), we get 2 foci and 2 directrices.
A hyperbola is a conic section, whose eccentricity is greater than 1. In other words, if is a focus and is the directrix, then for any point ,
The standard equation of hyperbola is
 Hyperbola is NOT a closed curve, has 2 parts, which are mirror images of each other
 Symmetric about and axes
 Does not pass through the origin
 Intersection with axis – at and
 Does not intersect axis
 Foci : and , directrices :
 Difference of focal distances = = constant (We’ve used this as the condition for locus of a point)
 Length of latus rectum =
 Parametric Equations :
 Transverse axis has length , conjugate axis has length
 If , we get a rectangular hyperbola

Where can you see the hyperbolic shape?
I) The black lines on a basketball or the red lines on the baseball
II) Orbits of comets around the Sun (or any star)
III) Interference patterns by 2 circular waves
IV) Potato chips (:P)
V) Cooling towers in an industrial plant
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