Fewpal
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Find the centroid of the triangle formed by the lines 12x2 - 20xy + 7y2 = 0 and 2x - 3y + 4 = 0

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We have

12x2 - 20xy + 7y2 ≡(2x - y)(6x - 7y)

 Therefore, the sides of the triangle are

2x - y = 0 ......(1)

6x - 7y = 0   .....(2)

2x - 3y = -4   ......(3)

Solving Eqs. (1) and (2), we get (1,2) as the vertex. Solving Eqs. (2) and (3), we obtain (7, 6) as another vertex.By hypotheses, (0, 0) is the third vertex. Hence, the centroid of the triangle is

(0 + 1 + 7/3 , 0 + 2 + 6/3) = (8/3,8/3)

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