Question:
If the line $\frac{x-2}{3} = \frac{y+1}{2} = \frac{z-1}{-1}$ intersect the curve $xy = c^{2}$ in XY-plane than $c = $
If the line $\frac{x-2}{3} = \frac{y+1}{2} = \frac{z-1}{-1}$ intersect the curve $xy = c^{2}$ in XY-plane than $c = $
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For any intersection with the XY-plane, always start by setting $z=0$.
Updated On: Jul 3, 2026
- $\pm 1$
- $\pm 3$
- $\pm \sqrt{5}$
- $\pm \sqrt{3}$
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The Correct Option is B
Solution and Explanation
Step 1: Concept
In the XY-plane, $z = 0$.
Step 2: Meaning
Substitute $z = 0$ into the line equation: $\frac{x-2}{3} = \frac{y+1}{2} = \frac{0-1}{-1} = 1$.
Step 3: Analysis
From $\frac{x-2}{3} = 1 \Rightarrow x - 2 = 3 \Rightarrow x = 5$. From $\frac{y+1}{2} = 1 \Rightarrow y + 1 = 2 \Rightarrow y = 1$.
Step 4: Conclusion
Substitute $x=5, y=1$ into $xy = c^2$: $5(1) = c^2 \Rightarrow c^2 = 5 \Rightarrow c = \pm \sqrt{5}$. Final Answer: (B)
In the XY-plane, $z = 0$.
Step 2: Meaning
Substitute $z = 0$ into the line equation: $\frac{x-2}{3} = \frac{y+1}{2} = \frac{0-1}{-1} = 1$.
Step 3: Analysis
From $\frac{x-2}{3} = 1 \Rightarrow x - 2 = 3 \Rightarrow x = 5$. From $\frac{y+1}{2} = 1 \Rightarrow y + 1 = 2 \Rightarrow y = 1$.
Step 4: Conclusion
Substitute $x=5, y=1$ into $xy = c^2$: $5(1) = c^2 \Rightarrow c^2 = 5 \Rightarrow c = \pm \sqrt{5}$. Final Answer: (B)
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