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Find the equation of the circle passing through the points 11,11, 22,1-1& 33,22

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z , 7 Years ago
Grade 11
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Lakshay Kumar

Last Activity: 7 Years ago

Let the equation of the general form of the required circle be x^2 + y^2 + 2gx + 2fy + c = 0 ……………. iAccording to the problem, the above equation of the circle passes through the points 1, 1, 2, -1 and 3, 2. Therefore,1 + 1 + 2g + 2f + c = 0 2 + 2g + 2f +c = 0……………. ii4 +1 + 4g - 2f+ c = 0 5 + 4g - 2f + c = 0……………. iii9 + 4 + 6g + 4f + c = 0 13 + 6g + 4f + c = 0……………. ivOn solving ii and iii, and iii and ivWe obtain c = 4, g = -5/2 and f = -1/2Substituting the values of g, f and c in i, we obtain the equation of the required circle as x^2 + y^2 - 5x - y + 4 = 0

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