SATHEE: Straight Line and Pair of Straight Lines 1 Question 57

Straight Line and Pair of Straight Lines 1 Question 57

57. Find the equations of the line passing through the point $(2, 3)$ and making intercept of length 3 unit between the lines $y + 2 x = 2$ and $y + 2 x = 5$ .

(1991, 4M)

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Solution:

Let $l$ makes an angle $α$ with the given parallel lines and intercept $A B$ is of 3 units.

Now, distance between parallel lines

$\begin{aligned} = \frac{| 5 - 2 |}{\sqrt{1^{2} + 2^{2}}} = \frac{3}{\sqrt{5}} \\ ∴ \sin α & = \frac{1}{\sqrt{5}}, \cos α = \frac{2}{\sqrt{5}} \\ , and \tan α & = \frac{1}{2} \end{aligned}$

$\Rightarrow$ Equation of straight line passing through $(2, 3)$ and making an angle $α$ with $y + 2 x = 5$ is

$\begin{aligned} \frac{y - 3}{x - 2} & = \tan (θ + α) \\ and & \frac{y - 3}{x - 2} & = \frac{\tan θ + \tan α}{1 - \tan θ \tan α} \\ \Rightarrow & \frac{y - 3}{x - 2} & = \frac{\tan θ - \tan α}{1 + \tan θ \tan α} \\ \Rightarrow & \frac{y - 3}{x - 2} & = - \frac{3}{4} and \frac{y - 3}{x - 2} = \frac{1}{0} \end{aligned}$

Straight Line and Pair of Straight Lines 1 Question 57

57. Find the equations of the line passing through the point $(2, 3)$ and making intercept of length 3 unit between the lines $y + 2 x = 2$ and $y + 2 x = 5$ .

Solution:

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Straight Line and Pair of Straight Lines 1 Question 57

57. Find the equations of the line passing through the point (2,3) and making intercept of length 3 unit between the lines y+2x=2 and y+2x=5.

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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57. Find the equations of the line passing through the point $(2, 3)$ and making intercept of length 3 unit between the lines $y + 2 x = 2$ and $y + 2 x = 5$ .