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



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