Distance between Parallel Lines MCQ Quiz in বাংলা - Objective Question with Answer for Distance between Parallel Lines - বিনামূল্যে ডাউনলোড করুন [PDF]

Concept:

The distance between the parallel lines ax + by + c₁ and ax + by + c₂ is:

D = \(\rm \left|c_1-c_2\over\sqrt{a^2+b^2}\right|\)

Calculation;

The 2 given lines are:

3y + 4x - 12 = 0

3y + 4x - 7 = 0

a = 4, b = 3, c₁ = -12 and c₂ = -7

∴ The distance between the lines

D = \(\rm \left|c_1-c_2\over\sqrt{a^2+b^2}\right|\)

⇒ D = \(\rm \left|-12-(-7)\over\sqrt{4^2+3^2}\right|\)

⇒ D = \(\rm \left|-5\over5\right|\) = 1

Concept:

The distance between two parallel lines ax + by + c₁ = 0 and ax + by + c₂ = 0 is given by the formula: \(\rm d=\dfrac{|c_1-c_2|}{\sqrt{a^2+b^2}}\).

Calculation:

Using the concept above, we have a = 5, b = -12, c₁ = 2 and c₂ = -3.

∴ \(\rm d=\dfrac{|c_1-c_2|}{\sqrt{a^2+b^2}}\)

= \(\rm \dfrac{|2-(-3)|}{\sqrt{5^2+(-12)^2}}\)

= \(\rm \dfrac{|5|}{\sqrt{169}}\)

= \(\dfrac{5}{13}\).