Question
Download Solution PDFयदि एक वृत्त का केंद्र (2, 3) पर है और वह दूसरे वृत्त x2 + y2 + 4x - 8y + 16 = 0 को लंबकोणतः प्रतिच्छेदित करता है तो वृत्त का समीकरण क्या होगा?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा :
लांबिकता की स्थिति = 2g1g2 + 2f1f2 = c1 + c2
गणना:
माना कि उस लांबिक वृत्त का समीकरण x2 + y2 + 2gx + 2fy + c = 0 है
दिया हुआ: वृत्त का केंद्र (2, 3) है और यह एक और वृत्त x2 + y2 + 4x - 8y + 16 = 0 को लंबकोणतः प्रतिच्छेदित करता है।
तो g1 = - 2, f1 = - 3, g2 = 2, f2 = - 4, c1 = c और c2 = 16
दिए गए वृत्त के साथ लांबिकता की स्थिति को लागू करके -
⇒ 2( - 2)(2) + 2.( - 3). ( - 4) = c + 16
⇒ c = 0
तो वांछित समीकरण x2 + y2 - 4x - 6y = 0 होगा
Last updated on Jun 20, 2025
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