Mathematics - Straight line Question with Solution | TestHub

Equation of the line making intercepts a and $b$ on the axes is $\frac{x}{a}+\frac{y}{b}=1$ Since, it passes through (1,1) $\Rightarrow \frac{1}{\mathrm{a}}+\frac{1}{\mathrm{b}}=1$ Also the area of the triangle formed by the line and the axes is $\mathrm{A}$. $\therefore \frac{1}{2}\mathrm{ab}=\mathrm{A}\Rightarrow \mathrm{ab}=2\mathrm{A}$ From eqs. (i) and (ii), we get, $a+b=2A$ Hence, a and b are the roots of the eq. $x^2-(a+b)x+ab=0\Rightarrow x^2-2Ax+2A=0$