Question:

Let d be the distance between the parallel lines 3x - 2y + 5 = 0 and 3x - 2y + 5 + 2√13 = 0. Let L1 = 3x - 2y + k1 = 0 (k1 > 0) and L2 = 3x - 2y + k2 = 0 (k2 > 0) be two lines that are at the distance of \(\frac{4d}{√13}\) and \(\frac{3d}{√13}\) from the line 3x - 2y + 5y = 0. Then the combined equation of the lines L1 = 0 and L2 = 0 is:

Updated On: May 9, 2024

  • (3x - 2y)2 + 24(3x - 2y) + 143 = 0

  • (3x - 2y)2 + 8(3x - 2y)+ 33 = 0

  • (3x - 2y)2 +12(3x-2y) + 13 = 0

  • (3x - 2y)2 +12(3x-2y) + 1 = 0

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The Correct Option is A

Solution and Explanation

The correct option is (A) (3x - 2y)2 + 24(3x - 2y) + 143 = 0

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Concepts Used:

Coordinate Geometry

Coordinate geometry, also known as analytical geometry or Cartesian geometry, is a branch of mathematics that combines algebraic techniques with the principles of geometry. It provides a way to represent geometric figures and solve problems using algebraic equations and coordinate systems.
The central idea in coordinate geometry is to assign numerical coordinates to points in a plane or space, which allows us to describe their positions and relationships using algebraic equations. The most common coordinate system is the Cartesian coordinate system, named after the French mathematician and philosopher René Descartes.