Quadratic Representation of Pair of Straight Lines/Examples/x^2 + y^2 - 1 = 0
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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.
$\blacksquare$
Sources
- 1933: D.M.Y. Sommerville: Analytical Conics (3rd ed.) ... (previous) ... (next): Chapter $\text {II}$. The Straight Line: $13$. Quadratic equation representing a pair of straight lines