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If the equation ax^2+2hxy+by^2+2gx+2fy+c...

If the equation `ax^2+2hxy+by^2+2gx+2fy+c=0` represents a pair of lines, then show that the square of the distance of their point of intersection from the origin is `(c(a+b)-f^2-g^2)/(ab-h^2)`. Also show that the square of this distance is `(f^2+g^2)/(h^2+b^2)` if the given lines are perpendicular.

Text Solution

Verified by Experts

The correct Answer is:
`(f^(2)+g^(2))/(h^(2)+b^(2))`.
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