SATHEE: Straight Line and Pair of Straight Lines 1 Question 1

Straight Line and Pair of Straight Lines 1 Question 1

1. A straight line $L$ at a distance of 4 units from the origin makes positive intercepts on the coordinate axes and the perpendicular from the origin to this line makes an angle of $60^{\circ}$ with the line $x + y = 0$ . Then, an equation of the line $L$ is

(2019 Main, 12 April II)

(a) $x + \sqrt{3} y = 8$

(b) $(\sqrt{3} + 1) x + (\sqrt{3} - 1) y = 8 \sqrt{2}$

(d) $(\sqrt{3} - 1) x + (\sqrt{3} + 1) y = 8 \sqrt{2}$

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Solution:

According to the question, we have the following figure.

Let $θ$ be the inclination of the line $x + y = 0$ . Then,

$\begin{array}{cc} \tan θ = - 1 = \tan (180^{\circ} - 45^{\circ}) \\ \Rightarrow & \tan θ = \tan 135^{\circ} \\ \Rightarrow & θ = 135^{\circ} \\ \Rightarrow & α + 60^{\circ} = 135^{\circ} \\ \Rightarrow & α = 75^{\circ} \end{array}$

Since, line $L$ having perpendicular distance $O M = 4$ .

So, equation of the line ’ $L$ ’ is

$\begin{array}{cc} x \cos α + y \sin α = 4 \\ \Rightarrow & x \cos 75^{\circ} + y \sin 75^{\circ} = 4 \\ \Rightarrow x \cos (45^{\circ} + 30^{\circ}) + y \sin (45^{\circ} + 30^{\circ}) = 4 \end{array}$

$\begin{aligned} \Rightarrow x \frac{\sqrt{3}}{2 \sqrt{2}} - \frac{1}{2 \sqrt{2}} + y \frac{\sqrt{3}}{2 \sqrt{2}} + \frac{1}{2 \sqrt{2}} = 4 \\ \Rightarrow (\sqrt{3} - 1) x + y (\sqrt{3} + 1) = 8 \sqrt{2} \end{aligned}$

Straight Line and Pair of Straight Lines 1 Question 1

1. A straight line $L$ at a distance of 4 units from the origin makes positive intercepts on the coordinate axes and the perpendicular from the origin to this line makes an angle of $60^{\circ}$ with the line $x + y = 0$ . Then, an equation of the line $L$ is

Solution:

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Straight Line and Pair of Straight Lines 1 Question 1

1. A straight line L at a distance of 4 units from the origin makes positive intercepts on the coordinate axes and the perpendicular from the origin to this line makes an angle of 60∘ with the line x+y=0. Then, an equation of the line L is

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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1. A straight line $L$ at a distance of 4 units from the origin makes positive intercepts on the coordinate axes and the perpendicular from the origin to this line makes an angle of $60^{\circ}$ with the line $x + y = 0$ . Then, an equation of the line $L$ is