73. Find equation of the line which is equidistant from parallel lines 9x + 6y – 7 = 0 and 3x + 2y + 6 = 0.

73. The given eqn of limes are.9x + 6y – 7 = 0 ______ (1)3x + 2y + b = 0 ______ (2)Let P (x0, y0) be a point equidistant from (1) and (2) so9x0 + 6y - 7 = ± 3 (3x0 + 2y0 + 6)When, 9x0 + 6y0 – 7 = 3 (3x0 + 2y0 + 6)⇒ 9x0 + 6y0 - 7 = 9x0 + 6y0 + 18⇒ - 7 = 18 which in not trueSo, 9x0 + 6y0 - 7 = -3 (3x0 + 2y0 + 6)⇒ 9x0 + 6y0 -7 = -9x0 -6y0 -18⇒ 18x0 + 12y0 + 11= 0.Hence, the required eqn of line through (x0, y0) & equidistant from parallel line 9x + 6y - 7 = 0and 3x + 2y + 6 = 0 is 18x + 12y + 11 = 0.

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73. Find equation of the line which is equidistant from parallel lines 9x + 6y – 7 = 0 and 3x + 2y + 6 = 0.

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alok kumar singh | Contributor-Level 10

4 months ago

73. The given eqⁿ of limes are.

9x + 6y – 7 = 0 ______ (1)

3x + 2y + b = 0 ______ (2)

Let P (x₀, y₀) be a point equidistant from (1) and (2) so

9x₀ + 6y - 7 = ± 3 (3x₀ + 2y₀ + 6)

When, 9x₀ + 6y₀ – 7 = 3 (3x₀ + 2y₀ + 6)

⇒ 9x₀ + 6y₀ - 7 = 9x₀ + 6y₀ + 18

⇒ - 7 = 18 which in not true

So, 9x₀ + 6y₀ - 7 = -3 (3x₀ + 2y₀ + 6)

⇒ 9x₀ + 6y₀ -7 = -9x₀ -6y₀ -18

⇒ 18x₀ + 12y₀ + 11= 0.

Hence, the required eqn of line through (x₀, y₀) & equidistant from parallel line 9x + 6y - 7 = 0

and 3x + 2y + 6 = 0 is 18x + 12y + 11 = 0.

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