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 x 0 b x 0 = 0. 1. Both the statements are true. 2. Both the statements are false. 3. Statement 1 is true, and statement 2 is false. 4. Statement 1 is false, and statement 2 is true.

Mathematics

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A line passes through the origin (0, 0) if the coordinates of the origin satisfy the equation of the line.

Substituting x = 0 and y = 0 in L.H.S. of the equation ax ± by = 0, we get :

⇒ a(0) ± b(0)

⇒ 0, which is equal to R.H.S.

Since, (0, 0) satisfies the equation ax ± by = 0, thus lines of the form ax ± by = 0 always pass through the origin.

∴ Both the statements are true.

Hence, option 1 is the correct option.

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