Q. 2 B5.0( 2 Votes )

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

y(t_{1} + t_{2}) = 2x + 2at_{1}t_{2}. y(t_{2} + t_{3}) = 2x + 2at_{2}t_{3} and, y(t_{3} + t_{1}) = 2x + 2at_{1}t_{3}.

Answer :

Given:

y (t_{1} + t_{2}) = 2x + 2a t_{1}t_{2}, y (t_{2} + t_{3}) = 2x + 2a t_{2}t_{3} and y (t_{3} + t_{1}) = 2x + 2a t_{1}t_{3}

To find:

Point of intersection of pair of lines.

Concept Used:

Point of intersection of two lines.

Explanation:

2x − y (t_{1} + t_{2}) + 2a t_{1}t_{2} = 0 … (1)

2x − y (t_{2} + t_{3}) + 2a t_{2}t_{3} = 0 … (2)

2x − y (t_{3} + t_{1}) + 2a t_{1}t_{3} = 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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