-2
$\begingroup$

If $ax^2+2hxy+by^2+2gx+2fy+c=0$ represents a pair of straight lines then show that the square of the distance from origin to their point of intersection is $\cfrac{c(a+b)-f^2-g^2}{ab-h^2}$

I could not figure out how to find the distance and how to show the required. Note; If you can please provide a solution with a figure.[IF POSSIBLE]

$\endgroup$
0

1 Answer 1

1
$\begingroup$

HINT: Begin with the straight lines $py+qx+r=0; sy+tx+u=0$ and compute their intersection. The conic is their product, so you can compute that too. It is a bit laborious, but should work straightforwardly.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged .