Question
Download Solution PDFयदि ax + by = c वृत्त x2 + y2 = 16 की स्पर्श रेखा है, तो निम्नलिखित में से कौन-सा सही है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
एक वृत्त की स्पर्श रेखा: एक बिंदु (a, b) पर वृत्त x2 + y2 = r2 की स्पर्श रेखा के समीकरण को ax + by = r2 द्वारा ज्ञात किया गया है।गणना:
वृत्त के सामान्य समीकरण अर्थात् x2 + y2 = r2 के साथ समीकरण x2 + y2 = 16 की तुलना करने पर, हमारे पास r2 = 16 है।
साथ ही, चूँकि रेखा ax + by = r2 वृत्त पर बिंदु (a, b) पर x2 + y2 = r2 की स्पर्श रेखा है, हम कह सकते हैं कि रेखा ax + by = c का x2 + y2 = 16 की स्पर्श रेखा होने के लिए (a, b) को वृत्त और c = r2 = 16 पर होना चाहिए।
∴ a2 + b2 = c
⇒ c(a2 + b2) = c2
⇒ 16(a2 + b2) = c2.
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