Question
Download Solution PDFदीर्घवृत्त 3x2 + y2 -12x + 2y + 1 = 0 के लैटस रेक्टम की लम्बाई क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
दीर्घवृत्त का मानक समीकरण:
लैटस रेक्टम की लम्बाई = जब a > b है, तो 2b2/a है और जब a < b है, तो 2a2/b है।
गणना:
3x2 + y2 -12x + 2y + 1 = 0
⇒ 3(x2 - 4x + 4) – 12 + (y2 + 2y + 1) = 0
⇒ 3(x – 2)2 – 12 + (y + 1)2 = 0
⇒ 3(x – 2)2 + (y + 1)2 = 12
∴ a2 = 22 और b2 = (2√3)2
यहाँ a < b
इसलिए, लैटस रेक्टम की लम्बाई = 2a2/b
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अतः विकल्प (3) सही है।
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