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+1 vote
26.0k views
in Co-ordinate geometry by (46.6k points)

If L1 and L2 are two lines belonging to family of lines (3 + 2λ) x + (4 + 3λ)y – 7 – 5λ = 0 (λ is parameter) such that it is at maximum and minimum distance from (2, 3), respectively, then the equation of lines passing through (1, 2) and making equal angles with L1 and L2 is/are

(A)  x + 2y = 7

(B)  3x + y = 5

(C)  x – 3y = –5

(D)  None of these 

1 Answer

+2 votes
by (52.7k points)
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Best answer

Given family of lines can be written as

3x + 4y – 7 +l(2x + 3y – 5) = 0

The point of intersection is (1, 1). Let Q ≡ (2, 3)

L1 will be perpendicular to PQ through P and L2 will be passing through Q. Therefore,

L1 ≡ 2y + x = 3 L2 ≡ 2x − y = 1 As angle between the line is same for L1 & L2. Therefore,

m1 = (1+ 2)/(1 - 2) = -3

Other slope will be perpendicular to m1, that is,

m2 = 1/3

So, equation of lines passing through (1, 2) are

3x + y = 5

x –3y = –5

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