Quadratic Representation of Pair of Straight Lines/Examples/x^2 + y^2 - 1 = 0

Examples of Quadratic Representation of Pair of Straight Lines

The equation:

$x^2 + y^2 - 1 = 0$

does not represent two straight lines embedded in the Cartesian plane.

Proof

$x^2 + y^2 - 1$ cannot be expressed in the form:

$\paren {l_1 x + m_1 y + n_1} \paren {l_2 x + m_2 y + n_2} = 0$

The result follows from Quadratic Representation of Pair of Straight Lines.

$\blacksquare$