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I cant get the final answer of this equation..i tried lot of things but i didnt get the right answer...how to solve this using the equation of a circle passing through three points?

nonuser
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Cem Nuiz
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    Welcome to stackexchange.This question is likely to be closed or downvoted because you show no effort. Just saying you "tried lots of things" is not enough. Edit the question to tell us carefully what you did try and where you are stuck. Use mathjax: https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference – Ethan Bolker Jul 06 '18 at 16:32
  • You should have a look at this question and the answers provided there. – sharding4 Jul 06 '18 at 16:38

2 Answers2

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Hint:

Notice that a triangle is right at $(1,3)$ so midpoint of a segment between $A(-1,2),B(2,1)$ is a center of a circle and $2r =AB=\sqrt{10}$.

nonuser
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Solving for the center $(a, b)$ and the radius $R$ with 3 equations may be a little tiring, so I suggest a more gradual approach:

  1. Find the equations of 2 chords formed from the following points.

  2. Find the equations of the perpendicular bisectors of the chords.

  3. Solve for the center by finding the intersection of the perpendicular bisectors.

  4. Solve for the radius by finding the distance between one of the given points and the center.

The equation of the circle is then

$$(x-a)^2+(y-b)^2=R^2$$

Matan Haller
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