The vertices of a $∆$ OBC are O (0, 0), B(–3, –1) and C(–1, –3). The equation of a line parallel to BC and intersecting sides OB and OC whose distance from the origin is $\frac{1}{2}$ , is

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

$x + y + \frac{1}{2} = 0$

$x + y + \frac{1}{\sqrt{2}} = 0$

$x + y - \frac{1}{\sqrt{2}} = 0$

$x + y - \frac{1}{2} = 0$

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

The equation of line BC is x + y + 4 = 0

$∴$ Equation of a line parallel to BC is x + y + k = 0

This is at a distance $\frac{1}{2}$ from the origin.

$∴ |\frac{k}{\sqrt{2}}| = \frac{1}{2}$

$∴ k = \pm \frac{1}{\sqrt{2}}$

Since BC and the required line are on the same side of the origin

$∴ k = \frac{1}{\sqrt{2}}$

Hence, the required line is $x + y + \frac{1}{\sqrt{2}} = 0$

Watch 3-min video & get full concept clarity