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| Homogenous equation of second degree in x and y represents a pair of straight lines passing through the origin |
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| To show that a homogenous equation of second degree in x and y represents a pair of straight lines passing through the origin |
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| The homogenous equation of second degree in x and y is given by |
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| ax2 + 2hxy + by2 = 0 where a, h, b are constants. |
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| Write ax2 + 2hxy + by2 = 0 …..(1) |
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| Multiply (1) by 4 times the co-efficient of x2 i.e., by 4a |
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| Adding (2hy)2 to both the sides, we get |
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are the two straight lines represented by (1). |
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| 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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