Ex 11.1, 3 - Equation of circle center (1/2, 1/4) radius 1/12   - Circle

  1. Chapter 11 Class 11 Conic Sections
  2. Serial order wise

Transcript

Ex 11.1, 3 Find the equation of the circle with centre 1 2 , 1 4 and radius 1 12 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) = 1 2 , 1 4 So h = 1 2 & k = 1 4 & radius (r) = 1 12 . Putting values in (1) x 1 2 2 + y 1 4 2 = 1 12 2 x2 + 1 2 2 2 x 1 2 + y2 + 1 4 2 2 y 1 4 = 1 144 x2 + 1 4 x + y2 + 1 16 1 2 y = 1 144 x2 + y2 x 1 2 y + 1 4 + 1 16 1 144 = 0 144 2 + 144 2 144 72 + 34 + 9 + 1 144 = 0 144x2 + 144y2 144x 72y + 44 = 0 144 144x2 + 144y2 144x 72y + 44 = 0 4(36x2 + 36y2 36x 18y + 11) = 0 36x2 + 36y2 36x 18y + 11 = 0 Hence the required equation of circle is 36x2 + 36y2 36x 18y + 11 = 0

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