Question

Consider the line 4x – 3y + 12 = 0

1. Find the equation of the line passing through the point (1, 2) and parallel to the given line. 

2. Find the distance between these two parallel lines. 

3. Which among the following lines is perpendicular to the line 4x – 3y + 12 = 0

• 2x + 3y – 8 = 0
• 4x – 3y + 5 = 0
• x + y = 7
• 3x + 4y + 9 = 0

Answer 1

1. Equation of the parallel line 4x – 3y + k = 0

Passing through (1, 2)

4(1) – 3(2) + k = 0 ⇒ k = 2

⇒ 4x – 3y + 2 = 0.

2. Distance \(|\frac{12-2}{\sqrt{25}}| = \frac{10}{5} = 2.\)

3. 3x + 4y + 9 = 0