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AP EAMCET20228 Jul 2022Morning ShiftMathematicsStraight LinesActual

Suppose a triangle of area 27 sq. units is formed by 18 x^2-9 x y+y^2=0 and y=c . Then the centroid of the triangle is

Options

  1. A(3,12)
  2. B(12,3)
  3. C(-12,3)
  4. D(-3,12)

Correct answer

A. (3,12)

Step-by-step solution

Let two lines 4= y = m , x and b = y m 18 x 2-9 x y+y 2=(y-m, x)(y-m, x) on complaining M ₁+ M ₂= g and M ₁, M ₂=18 M₁=3,6 M₂=6,3 hence equations are y=3 x, y=6 x now point of inter section of y=3 x, y=6 x and y=c will be (0,0) ( c 6 , c ) and ( c 3 , c ) now area of 1 2 c 6 c =27 (Given) C =18 Co ordinates will be (0,0),(3,18) and (6,18) now Centroid =(3,12)

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