Question

Find the condition that the general equation of the second degree may represent two straight lines.

Answer 1

The centre (bar x, bar y) of the conic is given by

Also, if it be transformed to the centre as origin, the equation becomes

Now the equation (3) represents two straight lines if c' be zero,

The equation therefore represents two straight lines if the relations (1), (2), and (4) be simultaneously true.

Eliminating the quantities bar x and bar y from these equations, we have,