Through the point (1$$, $$1), a straight line is drawn so as to form with coordinate axes a triangle of area S. The intercepts made by the line on the coordinate axes are the roots of the equation

Question

Infinity Learn · Accepted Answer

If a, b are the intercepts made by the line, then the equation of the line is $$xa+yb=1Since$$ it passes through (1$$, $$1), ∴   $$1a+1b=1$$⇒$$a+bab=1$$       $$----(1)Also$$, area of the triangle made by the straight line on the coordinate axes is S∴$$12ab=S$$ i,e., $$ab=2S$$  $$-----(2)So$$, by (1),  $$a+b=2S$$  $$-----(3)From$$ (2) and (3), the intercepts a and b are the roots of the equation $$x2-2Sx+2S=0$$.

Through the point (1, 1), a straight line is drawn so as to form with coordinate axes a triangle of area S. The intercepts made by the line on the coordinate axes are the roots of the equation

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