वक्र \(\rm x = \frac{y^2}{21}\) के नाभिलंब की लम्बाई क्या है?

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  1. 84 इकाई 
  2. 21 इकाई 
  3. \(\sqrt{21}\) इकाई 
  4. 21/4 इकाई 

Answer (Detailed Solution Below)

Option 2 : 21 इकाई 
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संकल्पना:

केंद्र पर शीर्ष और X - अक्ष के साथ परवलय का समीकरण: y= 4ax,

नाभिलंब की लम्बाई = 4a

 

गणना:

परवलय का मानक रूप: y= 4ax          ....(1)

हमारे पास निम्न हैं, \(\rm x = \frac{y^2}{21}\) \(\Rightarrow \rm y^2=21x\)

दिए गए समीकरण \(\rm y^2=21x\) की तुलना समीकरण (1) के साथ करने पर, हमें निम्न प्राप्त होता है,

4a = 21

∴ नाभिलंब की लम्बाई 21 इकाई है। 

अतः विकल्प (2) सही है।          

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