Question: If ab\> 0, ab\> 0 and the variable line $\frac{x}{a} + \frac{y}{b}$= 1 is drawn through the given...

Question

If ab> 0, ab> 0 and the variable line $\frac{x}{a} + \frac{y}{b}$ = 1 is drawn

through the given point P(a, b), then the least area of the triangle formed by this line and the co-ordinate axes is –

Answer 1

Let A (a, 0) and B(0, b) then area of DOAB = $\frac{1}{2}$

ab = $\frac{1}{2}\frac{a^{2}\beta}{a - \alpha}$ also $\left| \begin{matrix} a & 0 & 1 \\ 0 & b & 1 \\ \alpha & \beta & 1 \end{matrix} \right|$ = 0

Question: If ab\> 0, ab\> 0 and the variable line \(\frac{x}{a} + \frac{y}{b}\)= 1 is drawn through the given...