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Ex 11.1, 5 - Find circle centre (-a,-b) radius root a2-b2

Ex 11.1,  5 - Chapter 11 Class 11 Conic Sections - Part 2


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Ex 11.1, 5 Find the equation of the circle with centre (–a, –b) & radius √(a2 −b2) We know that equation of a circle is (x­ – h)2 + (y ­– k)2 = r2 Where (h, k) is the centre & r is the radius Here Centre (h, k) = (−a, −b) So h = −a & k = −b & Radius r = √(a2 −b2) . Putting values in (1) (x − (−a))2 + (y − (−b))2 = (√(a2 −b2))2 (x + a)2 + (y + b)2 = a2 − b2 x2 + a2 + 2ax + y2 + b2 + 2by = a2 – b2 x2 + y2 + 2ax + 2by + a2 + b2 = a2 – b2 x2 + y2 + 2ax + 2by + a2 + b2 − a2 + b2 = 0 x2 + y2 + 2ax + 2by + 2b2 = 0 Hence, the required equation is x2 + y2 + 2ax + 2by + 2b2 = 0

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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.