# Find the equation of a straight line passing through the point of intersection of x + 2y + 3 = 0 and 3x + 4y + 7 = 0 and perpendicular to the straight line x – y + 9 = 0.

Given:

x + 2y + 3 = 0 and 3x + 4y + 7 = 0

To find:

The equation of a straight line passing through the point of intersection of x + 2y + 3 = 0 and 3x + 4y + 7 = 0 and perpendicular to the straight line x – y + 9 = 0.

Explanation:

The equation of the straight line passing through the points of intersection of x + 2y + 3 = 0 and 3x + 4y + 7 = 0 is

x + 2y + 3 + λ(3x + 4y + 7) = 0

(1 + 3λ)x + (2 + 4λ)y + 3 + 7λ = 0

y

The required line is perpendicular to x y + 9 = 0 or, y = x + 9

λ = -1

Required equation is given below:

(1 3)x + (2 4)y + 3 7 = 0

x + y + 2 = 0

Hence, required equation is x + y + 2 = 0

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Various Forms of Equations of line45 mins
Slope, inclination and angle between two lines48 mins
Interactive Quiz on Equations of line23 mins
Parametric Equations of Straight line48 mins
Straight line | Analyse your learning through quiz56 mins
General Equation of a line43 mins
Motion in a Straight Line - 0665 mins
Motion in a Straight Line - 0556 mins
Motion in a Straight Line - 0372 mins
Understand The Interesting Concept Of Relative velocity in 1- Dimension44 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses