Question

A straight lines passes through the point P(2,6) and cuts the X-axis and Y-axis at A and B respectively, so that $\frac{AP}{BP}=\frac{2}{3}$ . the length of the y- intercept of the line is :

• A. 3.33
• B. 0.3
• C. 15
• D. 6.5

Answer 1

The correct option is C 15

Let the equation of required line be

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

Since the line cuts the cordinate axes at A and B so cordinate of A and B are (a,0) and (0,b) respectively.

As point P divides the line segment in ratio 2:3

Cordinates of P is (2,6)

$\therefore 2=\frac{0+3a}{5},6=\frac{2b+0}{5}$

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

So equation of line becames

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

So y-intercept is 15.