Question

Find the equation of a line which passes through the point (22, - 6) and is such that the intercept on x-axis exceeds the intercept on y-axis by 5.

Answer 1

$\text{Let equation of line be}\frac{x}{a}+\frac{y}{b}=1thena=b+5\therefore \frac{x}{b+5}+\frac{y}{b}=1\text{It passes through (22, -6)}\Rightarrow \frac{22}{b+5}-\frac{6}{b}=1\Rightarrow 22b-6b-30=b^2+5b\Rightarrow b^2-11b+30=0\Rightarrow b=5or6Now\text{when b = 5 then, a = 5 + 5 = 10}\text{when b = 6 then, a = 6 + 5 = 11}\therefore a=10or11\therefore \text{Equations of line are}\frac{x}{10}+\frac{y}{5}=1orx+2y-10=0and\frac{x}{11}+\frac{y}{6}=16x+11y=66$