Let $a$ and $b$ be two non-zero real numbers. The equation $(ax^2 + by^2 + c)(x^2 - 5xy + 6y^2) = 0$ represents:

  • A
    $A$ circle and an ellipse,when $a$ and $b$ are of the same sign and $c$ is of sign opposite to that of $a$.
  • B
    Two straight lines and a hyperbola,when $a$ and $b$ are of the same sign and $c$ is of opposite sign to $a$.
  • C
    Four straight lines,when $c = 0$ and $a, b$ are of the same sign.
  • D
    Two straight lines and a circle,when $a = b$ and $c$ is of sign opposite to that of $a$.

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