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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]

Mark Bennet
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Ger Wyn
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1 Answers1

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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.

Mark Bennet
  • 100,194