Geo2.8

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Find the equation of a straight line joining the points (at_{1}^{2},2at_{1}),(at_{2}^{2},2at_{2})\,

The equation of the required line is

y-2at_{1}={\frac  {2at_{2}-2at_{1}}{a(t_{2}+t_{1})(t_{2}-t_{1})}}\cdot (x-at_{1}^{2})\,

Simplifying

y-2at_{1}={\frac  {2}{t_{2}+t_{1}}}\cdot (x-at_{1}^{2})\,

(t_{1}+t_{2})(y-2at_{1})=2(x-at_{1}^{2})\,

2x-(t_{1}+t_{2})y+2at_{1}t_{2}=0\,


Main Page:Geometry:Straight Lines-I