﻿   Find the equation of the line passing through the point of intersection of the lines           x + 5y + 7 = 0, 3x + 2y – 5 = 0 and    1. parallel to the line 7x + 2y – 5 = 0 2. perpendicular to the line 7x + 2y – 5 = 0 : Kaysons Education

# Find The Equation Of The Line Passing Through The Point Of Intersection Of The Lines           x + 5y + 7 = 0, 3x + 2y – 5 = 0 And    1. Parallel To The Line 7x + 2y – 5 = 0 2. Perpendicular To The Line 7x + 2y – 5 = 0

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## Question

### Solution

Correct option is

2x – 7y – 20 = 0

Any line passing through the point of intersection of the given lines is

1. Line (i) is to be parallel to 7x + 2y – 5 = 0

Substituting this value of λ in equation (i), we get the required equation as 7x + 2y – 17 = 0

2. Line (i) is to be perpendicular to 7x + 2y – 5 = 0

Substituting this value of λ is eq. (i), we get the required equation as

2x – 7y – 20 = 0

Alternative Method : The point of intersection of the given lines

x + 5y – 7 = 0 and 3x + 2y – 5 = 0 is (3, –2)

∴ Equation of line through (3, –2) is

y + 2 = m(x – 3)                                    … (ii)

1. Line (ii) is parallel to 7x + 2y – 5 = 0

Hence the equation of the required line is

or    7x + 2y – 17 = 0

2. Line (ii) is perpendicular to 7x + 2y – 5 = 0

Hence the equation of the required line is

or     2x – 7y – 20 = 0

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