Prove that the line through the point (x₁, y₁) and parallel to the line Ax + By + C = 0 is A(x - x₁) + B (y - y₁) = 0

Solution:

The slope of line Ax + By + C = 0 or y = (- A/B)x + (- C/B) is m = - A/B

It is known that parallel lines have the same slope.

Therefore, slope of the other line = m = - A/B

The equation of the line passing through point (x₁, y₁) and having slope m = - A/B is

y - y₁ = m (x - x₁)

y - y₁ = - A/B (x - x₁)

B (y - y₁ = - A(x - x₁)

A(x - x₁) + B (y - y₁) = 0

Hence, the line through the point (x₁, y₁) and parallel to the line Ax + By + C = 0 is A(x - x₁) + B (y - y₁) = 0

NCERT Solutions Class 11 Maths Chapter 10 Exercise 10.3 Question 11

Prove that the line through the point (x₁, y₁) and parallel to the line Ax + By + C = 0 is A(x - x₁) + B (y - y₁) = 0

Summary:

The line through the point (x₁, y₁) and parallel to the line Ax + By + C = 0 is A(x - x₁) + B (y - y₁) = 0