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

  1. Chapter 11 Class 11 Conic Sections
  2. Serial order wise
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Ex 11.1, 5 Find the equation of the circle with centre (–a, –b) and 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 + 2(a)(x) + y2 + + b2 2(b)(y) = 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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