Question:
The distance between the parallel lines $5x + 12y - 3 = 0$ and $5x + 12y + 10 = 0$ is:
The distance between the parallel lines $5x + 12y - 3 = 0$ and $5x + 12y + 10 = 0$ is:
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Since $(5, 12, 13)$ is a standard Pythagorean triplet, the denominator $\sqrt{5^2+12^2}$ is instantly $13$. The difference in constants is $10 - (-3) = 13$. The distance is simply $13/13 = 1$.
Updated On: May 31, 2026
- $1$
- $2$
- $\frac{13}{17}$
- $\frac{7}{13}$
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The Correct Option is A
Solution and Explanation
Step 1: Concept
The perpendicular distance $d$ between two parallel lines $Ax + By + C_1 = 0$ and $Ax + By + C_2 = 0$ is given by: \[ d = \frac{|C_1 - C_2|}{\sqrt{A^2 + B^2}} \]
Step 2: Meaning
For the given parallel lines, we have $A = 5$, $B = 12$, $C_1 = -3$, and $C_2 = 10$.
Step 3: Analysis
Substituting the values into the formula: \[ d = \frac{|-3 - 10|}{\sqrt{5^2 + 12^2}} \] \[ d = \frac{|-13|}{\sqrt{25 + 144}} = \frac{13}{\sqrt{169}} = \frac{13}{13} = 1 \]
Step 4: Conclusion
The distance between the parallel lines is $1$ unit. Final Answer: (A)
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