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BodhiAI
Nov. 13, 2019

Pair of Tangent,Chord of Contact,chord bisected at a given point:

 

Equation of Pair of Tangents 

Let be any point which lies outside the hyperbola 

then the equation of pair of tangents drawn from this external point P to the hyperbola is given by

where,

{which is always positive as (x1,y1) lies outside the hyperbola}

Chord of Contact 

Let PA and PB be any two tangents to the hyperbola from some external in plane of the hyperbola.

Then, the line segment AB is known as the chord of contact and its equation is given by T = 0

Equation of Chord of Hyperbola if its Midpoint is Known

Let is the midpoint of the chord of the hyperbola  

then, the equation of chord of the hyperbola through this point is given by the equation T = S1