SOLUTION: Show that a pair of straight lines {{{ax^2+2hxy+ay^2+2gx+2fy+c=0}}} meet the co ordinate axes in concyclic points. Also find the equation of circle through those concyclic points.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Show that a pair of straight lines {{{ax^2+2hxy+ay^2+2gx+2fy+c=0}}} meet the co ordinate axes in concyclic points. Also find the equation of circle through those concyclic points.      Log On


   

Question 1016114: Show that a pair of straight lines ax%5E2%2B2hxy%2Bay%5E2%2B2gx%2B2fy%2Bc=0 meet the co ordinate axes in concyclic points. Also find the equation of circle through those concyclic points.
Found 2 solutions by ikleyn, fractalier:
Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
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Very interesting, but much higher than the school math.

Not for this site.


Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
This is similar to rotation-of-axes problems I have my students do in honors math analysis...
I can lend some expertise in that regard...the angle of rotation can be found via
cot (2*theta) = A-C / B where A = C = 1 and B = 2h
but the other tutor is right, this is beyond the level of this site...