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