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Ex 11.1, 7 - Find centre, radius of x2 + y2 - 4x - 8y - 45 = 0

Ex 11.1,  7 - Chapter 11 Class 11 Conic Sections - Part 2

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Transcript

Ex 11.1, 7 Find the centre and radius of the circle x2 + y2 – 4x – 8y – 45 = 0 Given x2 + y2 – 4x – 8y – 45 = 0. We need to make this in form (x – h)2 + (y – k)2 = r2 From (1) x2 – 4x + y2 – 8y = 45 (x2 – 2 (x) (2)) + (y2 – 2 (y) (4)) = 45 [x2 – 2(x)(2) + 22 – 22] + [y2 – 2(y)(4)+ 42 – 42] = 45 [x2 – 2(x)(2) + 22] + [y2 – 2(y)(4)+ 42] – 22 – 42 = 45 Using (a − b)2 = a2 + b2 − 2ab (x – 2)2 + (y – 4)2 – 4 – 16 = 45 (x – 2)2 + (y – 4)2 = 45 + 4 + 16 (x – 2)2 + (y – 4)2 = 65 Comparing (2) & (3) h = 2, k = 4 & r2 = 65 r = √65 Thus, Centre = (h, k) = (2, 4) And Radius = r = √𝟔𝟓

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.