Straight Lines
Family of Lines
Premium Question
Grade 11
Question:
If non-zero numbers $a, b, c$ are in H.P., then the straight line $\frac{x}{a} + \frac{y}{b} + \frac{1}{c} = 0$ always passes through a fixed point. That point is:
(1) $(1, -2)$
(2) $(-1, 2)$
(3) $(1, 2)$
(4) $(2, -1)$
Step-by-Step Solution
Key Concept: For H.P.: $1/a, 1/b, 1/c$ are in A.P., so $2/b = 1/a + 1/c$. Substitute the trial point $(1, -2)$ into the line equation and use the H.P. condition to verify.
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Correct Answer: (1)