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Locus of mid point of the portion between the axes of x +y =p where p is constant is

Options

  1. Ax^2+y^2= 4 p^2
  2. Bx^2+y^2=4 p^2
  3. C1 x^2 + 1 y^2 = 2 p^2
  4. D1 x^2 + 1 y^2 = 4 p^2

Correct answer

D. 1 x^2 + 1 y^2 = 4 p^2

Step-by-step solution

Equation of A B is x +y =p x p + y p =1 x p / + y p / =1 So co-ordinates of A and B are ( p , 0 ) and (0, p ) ; So coordinates of mid point of A B are ( p 2 , p 2 )= (x₁, y₁ )( let ) ; x₁= p 2 & y₁= p 2 =p / 2 x₁ and =p / 2 y₁ ; ^2 + ^2 =1 p^2 4 ( 1 x₁^2 + 1 y₁^2 )=1 Locus of (x₁, y₁ ) is 1 x^2 + 1 y^2 = 4 p^2 .

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