Q. 2 B5.0( 2 Votes )

Find the coordinates of the vertices of a triangle, the equations of whose sides are :

y(t1 + t2) = 2x + 2at1t2. y(t2 + t3) = 2x + 2at2t3 and, y(t3 + t1) = 2x + 2at1t3.

Answer :

Given:


y (t1 + t2) = 2x + 2a t1t2, y (t2 + t3) = 2x + 2a t2t3 and y (t3 + t1) = 2x + 2a t1t3


To find:


Point of intersection of pair of lines.


Concept Used:


Point of intersection of two lines.


Explanation:


2x − y (t1 + t2) + 2a t1t2 = 0 … (1)


2x − y (t2 + t3) + 2a t2t3 = 0 … (2)


2x − y (t3 + t1) + 2a t1t3 = 0 … (3)


Solving (1) and (2) using cross - multiplication method:





Solving (1) and (3) using cross - multiplication method:





Solving (2) and (3) using cross - multiplication method:





Hence, the coordinates of the vertices of the triangle are


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