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The foot of the perpendicular drawn from the origin, on the line, $3x+y=\lambda \left ( \lambda \neq 0 \right )$ is P. If the line meets x-axis at A and y-axis at B, then the ratio BP : PA is :

Option 1)
1 : 3

Option 2)
3 : 1

Option 3)
1 : 9

Option 4)
9 : 1

Answers (1)

best_answer

As we learned,

Selection formula -

$x= \frac{mx_{2}+nx_{1}}{m+n}$

$y= \frac{my_{2}+ny_{1}}{m+n}$

- wherein

If P(x,y) divides the line joining A(x₁,y₁) and B(x₂,y₂) in ration $m:n$

and

Slope – point from of a straight line -

$y-y_{1}=m(x-x_{1})$

- wherein

$m\rightarrow$ slope

$\left ( x_{1},y_{1} \right )\rightarrow$ point through which line passes

$x=\frac{\lambda }{3}\! A\left ( \frac{\lambda }{3},0 \right )$

and $x=0\: \Rightarrow \: y=\lambda$

$B\left ( 0,\lambda \right )$

$m_{oc}=\frac{1}{3}$

y - 0 = $\frac{1}{3}\left ( x-0 \right )$

$\Rightarrow$ 3y = x

and 3x + y = $\lambda$

$\Rightarrow$ 3(3y)+ $\lambda$ = $\lambda$

$\Rightarrow$ y = $\frac{\lambda }{10}$

$\frac{3\lambda }{10}=\frac{m\times 0+n\frac{\lambda }{3}}{m+n}$

$\Rightarrow \: \frac{n}{m}=\frac{9}{1}$

Option 1)

1 : 3

Option 2)

3 : 1

Option 3)

1 : 9

Option 4)

9 : 1

Posted by

Himanshu

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