Question

find the equation of a circle passing through the points (1,2),(3,5),(6,7)​

Answer 1

Step-by-step explanation:

Let point (1,2) be A , (3,−4) be B and (5,−6) be C

Let the mid point of AB be D=(2,−1) and the midpoint of BC be E=(4,−5)

The equation of line passing through D and perpendicular to AB is x−3y=5

The equation of line passing through E and perpendicular to BC is x−y=9

The center of circle is the point of intersection of above two lines which is equal to (11,2)

The radius of circle is 10

Therefore the equation of circle is (x−11)

2

+(y−2)

2

=100