Question
Download Solution PDFअतिपरवलय 9x2 - 25y2 = 225 के नाभिलंब की लम्बाई ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
अतिपरवलय:
|
समीकरण |
|
|
|
अनुप्रस्थ अक्ष का समीकरण |
y = 0 |
x = 0 |
|
संयुग्म अक्ष का समीकरण |
x = 0 |
y = 0 |
|
अनुप्रस्थ अक्ष की लम्बाई |
2a |
2a |
|
संयुग्म अक्ष की लम्बाई |
2b |
2b |
|
शीर्ष |
(± a, 0) |
(0, ± a) |
|
फोकस |
(± ae, 0) |
(0, ± ae) |
|
संचालिका |
x = ± a/e |
y = ± a/e |
|
केंद्र |
(0, 0) |
(0, 0) |
|
उत्केंद्रता |
|
|
|
नाभिलंब की लम्बाई |
|
|
|
बिंदु (x, y) की फोकस दूरी |
ex ± a |
ey ± a |
गणना:
दिया गया समीकरण, 9x2 - 25y2 = 225 है।
⇒
मानक समीकरण के साथ तुलना करने पर, a = 5 और b = 3
हम जानते हैं कि, नाभिलंब की लम्बाई
L.R =
L.R =
सही विकल्प 2 है।
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