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in Mathematics by (53.1k points)

Match the items of Column I with those of Column II.

Column I Column II
(A) The equation of the line perpendicular to 4x + y - 1 = 0 and passing through the intersection of the lines 2x + 5y + 3 = 0 and x - 3y - 7 = 0 is (p) 22x + 25y -  69 = 0
(B) The equation of the line passing through the intersection of the lines 3x - 2y + 10 = 0 and 4x + 3y 7 = 0 and also passing through the point (2, 1) is (q) x - 4y -  24 = 0
(C) Equation of the line which passes through the point (-2, -4) and has sum of its intercepts equal to 3 is (r) x - y 2y - 60 = 0 
D) A =(1,2), B = (3,4) and C = (2, 7). Equation of the line passing through A = (1,2) and perpendicular to the line BC is (t)  4x - y + 4 = 0

1 Answer

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(A)  Any line passing through the intersection of the lines 2x - 5y + 3 = 0 and x - 3y - 7 = 0 is of the form

This line is perpendicular to the line

Hence, the required line is

Answer: (A)  (q)

(B) The required line equation is of the form (3x - 2y + 10) + λ(4x + 3y - 7) = 0.This passes through the point (2, 1) which implies that

[3(2) -2(1) + 10] λ(8 + 3 - 7) = 0

14 + 4λ

λ = -7/2

Hence the required line is

Answer: (B)  (q)

(C) Let the line be

x/a + y/b = 1

Therefore

-2/a - 4/b = 1

or 4a + 2b = -ab   ....(1)

and  a + b = 3  ....(2)

Solving Eqs. (1) and (2), we have a = -1, b = 4 or a = 6 3 , ., b = -3

Answer: (C)  (r), (t)

(D) The slope of BC is

7 - 4/2 - 3 = -3

Hence, the equation of the line passing through A(1, 2) and perpendicular to the line BC is

y - 2 = 1/3(x - 1)

x - 3y + 5 = 0

Answer: (D)  (s)

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