How do you find the equation of a circle passing through (2,3), (3,4) and (-1,2)?

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Answer 1 · 2016-09-15T13:51:29

#" Eqn. of the circle : "x^2+y^2+2x-14y+25=0#.

There are more than one Methods to solve this problem.

I select the following one, which is the easiest in my opinion.

Let, the eqn. of the Circle be

# S : x^2+y^2+2gx+2fy+c=0,..(star)#, known as the General

Eqn. of Circle.

#" Pt. "(2,3) in S rArr 4+9+4g+6f+c=0.......(1)#

#" Pt. "(3,4) in S rArr 9+16+6g+8f+c=0......(2)#

#" Pt. "(-1,2) in S rArr 1+4-2g+4f+c=0.........(3)#

#(2)-(1) rArr 12+2g+2f=0..................(4)#

#(3)-(1) rArr -8-6g-2f+0..................(5)#

#(4)+(5) rArr 4-4g=0 rArr g=1." Now, "(4) rArr f=-7.#

# g=1, f=-7, &, (3) rArr c=25#.

Using all these consts. in #(star)#, we have, the eqn. of circle,

# S : x^2+y^2+2x-14y+25=0.#

Enjoy Maths.!