The equation of the chord of the circle ${x^2} + {y^2} = {a^2}$ having $({x_1},{y_1})$ as its mid-point is

  • [IIT 1983]
  • A

    $x{y_1} + y{x_1} = {a^2}$

  • B

    ${x_1} + {y_1} = a$

  • C

    $x{x_1} + y{y_1} = x_1^2 + y_1^2$

  • D

    $x{x_1} + y{y_1} = {a^2}$

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  • [JEE MAIN 2021]