Question

find the equation of circle passing through each of the following these points (2,1) (5,5)(-6,7)​

Answer 1

Answer:

Given: Three points  (2,1), (5,5), (-6,7).

To find: The equation of circle.

Solution:

Now the general equation of the circle is:

            x² + y² + 2gx + 2fy + c = 0 ……………. (i)

So according to the problem, the above equation of the circle passes through the points (2,1), (5,5), (-6,7). Therefore, the equations will be:

           for (2,1): 4 + 1 + 4g + 2f + c = 0

            5 + 4g + 2f + c = 0  .....................(ii)

           for (5,5): 25 + 25 + 10g + 10f + c = 0

            50 + 10g + 10f + c = 0 .................(iii)

           for (-6,7): 36 + 49 - 12g + 14f + c = 0

            85 - 12g + 14f + c = 0  ...................(iv)

Now iii - ii, we get:

            45 + 6g + 8f = 0 .................(v) Now iv - ii, we get:

            80 - 16g + 12f = 0 ...................(vi)

Now 2(vi) - 3(v), we get:

            160 - 32g + 24f - 135 - 18g - 24f = 0

            25 -50g = 0

            g = 25/50

            g = 1/2

Put g = 1/2 in vi, we get:

            80 - 16(1/2) + 12f = 0

            80 - 8 + 12f = 0

            12f = -72

            f = -72/12 = -6

Now putting f and g in ii, we get:

            5 + 4(1/2) + 2(-6) + c = 0

            c = -5 - 2 + 12

            c = 12 - 7

            c = 5

Therefore equation of circle is:

              x² + y² + x - 12y + 5 = 0

Answer:

        So the required equation of circle passing through (2,1), (5,5), (-6,7) is  x² + y² + x - 12y + 5 = 0

Step-by-step explanation:

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