Straight Line Equation Passing through the Origin

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The homogenous equation of second degree in x and y is given by

ax² + 2hxy + by² = 0 where a, h, b are constants.

Write ax² + 2hxy + by² = 0 …..(1)

Multiply (1) by 4 times the co-efficient of x² i.e., by 4a

Adding (2hy)² to both the sides, we get

are the two straight lines represented by (1).

These two equations are of the form y = m₁x and y = m₂x and therefore the given equation represents two straight lines through the origin. The two straight lines are real, coincident or imaginary