Straight Lines
Family of Lines
Premium Question
Grade 11
Question:
If $a, b, c$ are in A.P., then the straight line $ax + by + c = 0$ always passes through:
(1) $(1, -2)$
(2) $(-1, 2)$
(3) $(2, -1)$
(4) $(1, 2)$
Step-by-Step Solution
Key Concept: Write $c = 2b - a$ (A.P. condition) and substitute into $ax + by + c = 0$. Factor out $a$ and $b$ to find a point $(x_0, y_0)$ that satisfies the equation for all $a, b$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)