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# find the equation of circle passing through the points (1,1),(2,1)and (3,2)

SAGAR SINGH - IIT DELHI
879 Points
11 years ago

DEAR RAHUL,

The standard form of a circle whose centre is (g,f) and radius r is:
x² + y² -2gx -2gy + c = 0, where r² = g² + f² - c

First, 'plug in' the co-ords. of the first given point:
(1)² + (1)² -2g(1) - 2f(1) + c = 0
1+ 1 -2g -2f + c =0
2-2g-2f+c=0

Repeat for the next 2 given points. You obtain 3 simultaneous linear equations for g,f,c.
Solve them and 'plug' the values for g, f and c back into the standard equation.
Hence, the eq'n. of the circle is thus obtained.
{Incidentally, so is the radius: √[g² + f² -c] }

All the best.

Sagar Singh

B.Tech IIT Delhi

sagarsingh24.iitd@gmail.com