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Example 3 - Find centre, radius of circle x2 + y2 + 8x - Examples

Example  3 - Chapter 11 Class 11 Conic Sections - Part 2

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Example 3 Find the centre and the radius of the circle x2 + y2 + 8x + 10y – 8 = 0 Given x2 + y2 + 8x + 10y − 8 = 0 We need to make this in form (x – h)2 + (y – k)2 = r2 From (1) x2 + y2 + 8x + 10y − 8 = 0 (x2 + 8x) + (y2 + 10y) = 8 (x)2 + 2(4)(x) + y2 + 2(5)(y) = 8 [x2 + 2(4)(x) + (4)2 − (4)2] + [y2 + 2(5)(y) + (5)2 − (5)2] = 8 [x2 + 2(4)(x) + (4)2] + [y2 + 2(5)(y) + (5)2] − (4)2 − (5)2 = 8 (x + 4)2 + (y + 5)2 = 8 + 16 + 25 (x + 4)2 + (y + 5)2 = 49 (x – (– 4))2 + (y – (–5))2 = 72 Comparing (2) with (x – h)2 + (y – k)2 = r2 h = −4 , k = − 5 & r = 7 Thus, centre of circle = (h, k) = (−4, −5) & Radius = r = 7

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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.