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Analytical Geometry

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13 Oct 2007 00:44:27 IST

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how to find orthocentre using family of lines

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how to find orthocentre using family of lines???????

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Bipin Dubey

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Joined: 23 Jan 2007

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16 Oct 2007 11:29:57 IST

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Let the sides of the triangle be L₁=0, L₂=0, L₃=0.

Any line passing through L₁ and L₂ is : L₁ + k₁L₂ = 0
This line should be perpendicular to L₃ if it is to pass through the orthocentre.
Applying perpendicularity condition k₁ can be calculated.

Similarly L₂ + k₂L₃ = 0 is perpendicular to L₁ = 0 and we can find k₂ using perpendicularity condition.

Since k₁ and k₂ are known, we got two lines passing through orthocentre.
Now orthocentre can be found out by finding the intersection of the two lines.

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