Question
Download Solution PDFयदि A (4, 1) और B (-1, 4) से P (x, y) की दूरी बराबर हैं, तो निम्नलिखित में से कौन-सा सत्य है?
Answer (Detailed Solution Below)
Detailed Solution
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दो बिंदु (x1, y1) और (x2, y2) के बीच की दूरी 'd' को पाइथागोरस प्रमेय का प्रयोग करके प्राप्त किया गया है: d2 = (x1 - x2)2 + (y1 - y2)2.
गणना:
दो बिंदुओं के बीच की दूरी के लिए सूत्र का प्रयोग करने पर:
AP2 = (x - 4)2 + (y - 1)2
BP2 = (x + 1)2 + (y - 4)2
चूंकि दूरियां बराबर हैं, तो हमारे पास निम्न हैं:
AP2 = BP2
⇒ (x - 4)2 + (y - 1)2 = (x + 1)2 + (y - 4)2
⇒ x2 - 8x + 16 + y2 - 2y + 1 = x2 + 2x + 1 + y2 - 8y + 16
⇒ 10x = 6y
⇒ 5x = 3y.
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