Question

If the equation ax2+2hxy+by2+2gx+2fy+c=0 represents a pair of straight lines, then the square of the distance of their point of intersection from the origin is

Answer 1

For a general equation representing a pair of straight lines, the point of intersection is given as:

( (hf-bg)/ab-h^2), (gh-af/ab-h^2) )

Hence the square of distance of point of intersection from the origin is given as, sum of squares of x and y coordinates of the point of intersection.

(hf-bg)/ab-h^2)^2 + (gh-af/ab-h^2)^2