Question

Find the equation to the straight line which passes through the point (5, 6) and has intercepts on the axes

(i) equal in magnitude and both positive. (ii) equal in magnitude but opposite in sign.

Answer 1

$\text{(i) Intercepts are equal and positive}\Rightarrow a=b=k\text{The equation of straight line is}\frac{x}{a}+\frac{y}{b}=1...\left(i\right)\text{Since this line passes through (5, 6) and}\text{a = b = k, we get :}\frac{5}{k}+\frac{6}{k}=1k=1\therefore \frac{x}{11}+\frac{y}{11}=1\Rightarrow x+y=11\text{(ii) Intercepts are equal but opposite in sign}\text{Let, a = k, b = -k}\text{Putting in (1), we get}\frac{5}{k}+\frac{6}{-k}=1\frac{5}{k}-\frac{6}{k}=1\Rightarrow k=-1\text{Thus from (1)}x-y=-1$