अतिपरवलय के फोकस के निर्देशांक क्या हैं?

  1. (± 5, 0)
  2. (± 4, 0)
  3. (± 3, 0)
  4. इनमें से कोई नहीं 

Answer (Detailed Solution Below)

Option 1 : (± 5, 0)
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Detailed Solution

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संकल्पना:

एक अतिपरवलय का मानक समीकरण:  (a > b)

  • फोकस के निर्देशांक = (± ae, 0)
  • उत्केंद्रता (e) =  ⇔ a2e2 = a2 + b2
  • नाभिलंब की लम्बाई = 

 

गणना:

दिया गया है: 

अतिपरवलय के मानक समीकरण के साथ तुलना करने पर: 

इसलिए, a2 = 16 और b2 = 9

⇒ a = 4 और b = 3   (a > b)

अब, उत्केंद्रता (e) =  

फोकस के निर्देशांक = (± ae, 0) 

= (± 5, 0)

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