Question

Find the equation to the straight line which cuts off equal positive intercepts on the axes and their product is 25.

Answer 1

$\text{Let the intercepts on the axes be (a, 0) and (0, a)}\text{Then,}a\times a=25a^2=25a=5\text{(Ignoring negative sign because it is given that the intercepts are positive)}\Rightarrow a=b=5\text{(given the intercepts are equal)}\therefore \text{Putting in equation of straight line}\frac{x}{a}+\frac{y}{b}=1\frac{x}{5}+\frac{y}{5}=1x+y=5$