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BodhiAI
Nov. 8, 2019

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

 

Equation of Pair of Tangents

Let P (x1,y1)be any point outside the parabola then the equation of pair of tangents drawn from this external point P to the parabola is given by 

SS1=T2

where,

() which is always positive as

lies outside the parabola

Let (h, k) be the mid-point of PQ. Then,

 

 

Thus, the locus of (h, k) is which represents a straight line parallel to the axis of the parabola.

Chord of Contact

Let PA and PB be any two tangents to the parabola from some external point in the plane of parabola Then the line segment AB is known as chord of contact and its equation is given by

Equation of Chord of Parabola if its Mid Point is Known

Let - is the midpoint of chord of the parabola then the equation of chord of the parabola through this point is given by the equation