First slide

Equation of line in Straight lines

Question

The foot of the perpendicular on the line $3 x + y = λ$ drawn from the origin is C. If the line cuts the x-and the y-axis at A and B, respectively, then $BC : CA$ is

Moderate

A

1:3
B

3:1
C

1:9
D

9:1

Solution

$\tan (180^{0} - θ) =$ slope of AB=-3
$tanθ = 3$
$∴ \frac{OC}{AC} = tanθ, \frac{OC}{BC} = cotθ$
or $\frac{AC}{BC} = \frac{tanθ}{cotθ} = \tan^{2} θ = 9$

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