Question

Find the equation of the straight line which passes through the point P(2, 6) and cuts the coordinate axes at the point A and B respectively so that $\frac{AP}{BP}=\frac{2}{3}.$

Answer 1

$\text{The equation of the line with intercepts}$

$\text{a and b is}\frac{x}{a}+\frac{y}{b}=1$

$\text{Since, the line meets the coordinate axes at A and B, the coordinates of A and B are A (a, 0) and B (0, b).}$

$Given:AP:BP=2:3$

$Here,P=(2,6)$

$\therefore 2=\frac{2\times 0+3\times a}{2+3},6=\frac{2\times b+3\times 0}{2+3}$

$\Rightarrow 3a=10,2b=30$

$\Rightarrow a=\frac{10}{3},b=15$

$\text{Thus, the equation of the line is}$

$\frac{x}{\frac{10}{3}}+\frac{y}{15}=1$

$\Rightarrow \frac{3x}{10}+\frac{y}{15}=1$

$\Rightarrow 9x+2y=30$