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AP EAMCET202123 Aug 2021Evening ShiftMathematicsStraight LinesActual

Given points, A(6,0), B(0,4) and O as the origin, find the locus of a point P such that area of P O B is 2 times the area of P O A .

Options

  1. Ax^2-3 y^2=0
  2. Bx^2+3 y^2=0
  3. Cx^2-9 y^2=0
  4. Dx^2-4 y^2=0

Correct answer

C. x^2-9 y^2=0

Step-by-step solution

Given points, Let P be (x, y) ar ( P O B)=2 ar ( P O A) ...(i) Now, ar ( P O B) aligned & = 1 2 |x₁ (y₂-y₃ )+x₂ (y₃-y₁ )+x₃ (y₁-y₂ ) | & = 1 2 |x(0-4)+0+0| & =2 x aligned ar ( P O A)= 1 2 |x(0-0)+0+6(y-0)|= 3 y From Eq. (i), we get 2 x= 2 3 y x= 3 y Hence, the required locus of both the parts is (x-3 y)(x+3 y)=0 x^2-9 y^2=0

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