Question

Statement (1): The lines of the form ax ± by = 0 always pass through the origin.

Statement (2): On substituting x = 0 and y = 0; we get a × 0 ± b × 0 = 0.

Options

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true, and statement 2 is false.

• Statement 1 is false, and statement 2 is true.

Answer 1

Both the statements are true.

Explanation:

A linear equation in the form ax ± by = 0 has no constant term. Substituting x = 0 and y = 0 satisfies the equation (a × 0 ± b × 0 = 0), meaning every such line passes through the origin (0, 0). Thus, both statements are true.