GEOMETRY QUESTION How to find the equation of two lines of which the second degree joint equation is given?

2017-03-19 3:02 am

Is it possible only for some special cases in which we can factorize the equation evidently or generally with any second degree joint equation

回答 (1)

Sqdancefan

2017-03-19 5:17 am

✔ 最佳答案

If the equation is of two lines, it can always be factored.

The second-degree terms can be factored using the techniques applicable to trinomial quadratic expressions (including the quadratic formula). Using the found values of a, b, d, e, you can write two equations in c and f using the coefficients of the linear terms.
.. (ax +by +c)*(dx +ey +f)
.. = adx^2 +(ae+bd)xy +bey^2 +(af+cd)x +(bf+ce)y +cf

You could also pick a couple of x-values and find the corresponding y-values. If you assume small changes in one result in small changes of the other, you will have sufficient points to write the equations for the lines.

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