Find The Equation Of The Circle Passing Through The Three Non-collinear Points (1, 1), (2, –1) And (3, 2).

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Question

Find the equation of the circle passing through the three non-collinear points (1, 1), (2, –1) and (3, 2).

Solution

Correct option is

x2 + y2 – 5x – y + 4 = 0

 

Let the equation of circle be

                   x2 + y2 + 2gx + 2fy + c = 0                            …(1)

since the three given points lie on circle (1), we get 

         1 + 1 + 2g + 2f + c = 0   or   2g + 2f + c + 2 = 0     …(2)

         4 + 1 + 4g – 2f + c = 0   or   4g – 2f + c + 5 = 0      …(3)

         9 + 4 + 6g + 4f + c = 0   or   6g + 4f + c + 13 = 0   …(4)

Subtracting (2) from (3) and subtracting (3) from (4), then

                  2g – 4f + 3 = 0               …(5)

and            2g + 6f + 8 = 0               …(6)

solving (5) and (6), we get   

Now from (2), 

∴                    c = 4

Hence from (1), equation of circle is 

             x2 + y2 – 5x – y + 4 = 0

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SIMILAR QUESTIONS

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Q2

 

Find the area of an equilateral triangle inscribed in the circle

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Q3

 

Find the parametric form of the equation of the circle

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Q4

 

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(ii) x = a cos α + b sin α and y = a sin α – b cos α

Find its Cartesian form.
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Q6

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Q10

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