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AP EAMCET202419 May 2024Evening ShiftMathematicsHyperbolaActual

The locus of the mid points of the chords of the hyperbola x^2-y^2=a^2 which touch the parabola y^2=4 a x is

Options

  1. Ax (y^2-x^2 )=a y^2
  2. Bx (x^2+y^2 )=y^2+x
  3. Ca x^3+y^3=3 x
  4. Dx (x^2-y^2 )=a^2

Correct answer

A. x (y^2-x^2 )=a y^2

Step-by-step solution

Let mid point of the chord of the given parabola is ( , ) equation of chord is x x₁-y y₁=x₁^2-y₁^2...(i) x- y= ^2- ^2 y= ^2- ^2 + x Now, this equation touches to the parabola y^2=4 a x So, - ( ^2- ^2 ) = a - (x^2-y^2 ) x=a y^2 (y^2-x^2 ) x=a y^2

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