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find the equation of the circle through (-2,-4), (6,0) and (1,5)

find the equation of the circle through (-2,-4), (6,0) and (1,5)

Grade:12th pass

3 Answers

Sourabh Singh IIT Patna
askIITians Faculty 2104 Points
6 years ago

FInd out equations of two chords using three points. Then find the pair of equations of perpendicular bisectors. Find their point of intersection that will be centre . Find out the value of centre using centre and another point. Now you can find out the equation of centre.
12 Points
6 years ago
use general equation of circle...x2+y2+2gx+2fy+c=0 put the given coordinates and you will ger the linear eqn with three variables ...solve them to find g f c then put it on the general eqn 
Kaustubh Nayyar
27 Points
6 years ago
hey I have a simpler and unique solution      Use family of circles passing through two points and then put third point to get the constant
The required circle’s equation will be    S + k L = 0
where S is equation of circle passing through any two points ( lets say (6,0) and ( – 2, – 4) ) as diametric points   k is the constant we have to find  and L = 0 is the equation of diameter.
hence eq. of reqd. circle will be
(x – 6)(x + 2 ) + (y – 0)(y + 4 )  + k (2y – x + 6 ) = 0
Now,  ( 1, 5) lies on the reqd. circle
hence we get k = – 2
therefore, eq of reqd. circle   (x – 6)(x + 2 ) + (y – 0)(y + 4 ) – 2 (2y – x + 6 ) = 0
which gives   x2 + y2 – 2x – 24 = 0 
( this is a unique solution , you cannot find this method in books )

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