Question

find the equation of the circle passing through the points 5,7 8,1 1,3​

Answer 1

Step-by-step explanation:

apply (x-a) sq +( y-b) sq = r sq

put x, y

Answer 2

Given : points ((5,7) , (8,1) and (1,3)

To find : equation of the circle passing through the points

Solution :

The general equation of the circle is

x² +y²+2gx+2fy+c=0 ...(i)

therefore ,

5²+7² +2g(5) +2f(7) +c=0

74 + 10 g +14f +c=0 ..(1)

similarly

8²+1²+2g(8)+2f(1) +c=0

65 + 16 g +2f+c =0..(2)

and

1²+3²+2g(1) +2f(3) =0

10+2g+6f+c=0..(3)

solving equations 1 ,2 and 3 we get

$g = \frac{-29}{6}\\\\f = \frac{-19}{6}$

now , substituting the values of g and f in equation 1 we get

$c= \frac{56}{3}$

thus ,

equation (i) becomes

$x^2+y^2+2(\frac{-29}{6})x+2(\frac{-19}{6})+\frac{56}{3}=0\\\\3x^2+3y^2-29x-19y+56=0$

hence ,

the required equation is $3x^2+3y^2-29x-19y+56=0$

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