Question

find an equation of the circle passing through the points (5 6) (−3 2) and (3 4)

Answer 1

Let P (x1, y1), Q (x2, y2) and R (x3, y3) are the three given points.

We have to find the equation of the circle passing through the points P, Q and R.

Circle Passing Through Three Given Points

Circle Passing Through Three Given Points

Let the equation of the general form of the required circle be x2 + y2 + 2gx + 2fy + c = 0 ……………. (i)

According to the problem, the above equation of the circle passes through the points P (x1, y1), Q (x2, y2) and R (x3, y3). Therefore,

x12 + y12 + 2gx1 + 2fy1 + c = 0 ……………. (ii)

x22 + y22 + 2gx2 + 2fy2 + c = 0 ……………. (iii)

and x32 + y32 + 2gx3 + 2fy3 + c = 0 ……………. (iv)

Form the above there equations (ii), (iii) and (iv) find the value of g, f and c. Then substituting the values of g, f and c in (i) we can find the required equation of the circle.