16:I[8216,["972","static/chunks/972-b28da0de92681928.js","47","static/chunks/47-a7f06e9eda1ac756.js","115","static/chunks/app/%5Bexam%5D/questions/%5Byear%5D/%5Bsubject%5D/%5Bchapter%5D/%5BquestionId%5D/page-7b6f0a12b9cc0206.js"],"BackButton"] 17:I[1553,["972","static/chunks/972-b28da0de92681928.js","47","static/chunks/47-a7f06e9eda1ac756.js","115","static/chunks/app/%5Bexam%5D/questions/%5Byear%5D/%5Bsubject%5D/%5Bchapter%5D/%5BquestionId%5D/page-7b6f0a12b9cc0206.js"],"QuestionViewer"] 15:T4fb,{"@context":"https://schema.org","@type":"Quiz","name":"Jee Main 2021 Circle PYQ with Solution","url":"https://pyq-test-series-platform-alsjdcxu2-sameers-projects-41c5a71e.vercel.app/jee-main/questions/2021/mathematics/circle/1kru4cxvo","educationalLevel":"Entrance exam preparation","about":"Jee Main / Mathematics / Circle","hasPart":{"@type":"Question","name":"Jee Main 2021 Circle PYQ with Solution","text":"Let the circle S : 36x 2 + 36y 2 - 108x + 120y + C = 0 be such that it neither intersects nor touches the co-ordinate axes. If the point of intersection of the lines, x - 2y = 4 and 2x - y = 5 lies inside the circle S, then :","eduQuestionType":"mcq","acceptedAnswer":{"@type":"Answer","text":"D"},"comment":{"@type":"Comment","text":"S : 36x 2 + 36y 2 - 108x + 120y + C = 0 \\Rightarrow x 2 + y 2 - 3x + {{10} \\over 3}y + {C \\over {36}} = 0 Centre \\equiv ( - g, - f) \\equiv \\left( {{3 \\over 2},{{ - 10} \\over 6}} \\right) radius = r = \\sqrt {{9 \\over 4} + {{100} \\over {36}} - {C \\over {36}}} Now, \\Rightarrow r < {3 \\over 2} \\Rightarrow {9 \\over 4} + {{100} \\over {36}} - {C \\over {36}} < {9 \\over 4} \\Rightarrow C > 100 ...... (1) Now, point of intersection of x - 2y = 4 and 2x - y = 5 is (2, -1), which lies inside the circle S. \\t..."}}}18:T527,S : 36x² + 36y² $$-$$ 108x + 120y + C = 0

$$\Rightarrow$$ x² + y² $$-$$ 3x + $${{10} \over 3}$$y + $${C \over {36}}$$ = 0

Centre $$ \equiv ( - g, - f) \equiv \left( {{3 \over 2},{{ - 10} \over 6}} \right)$$<

Circle

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