Question

Consider a circle passing through the origin and the points (a,b) and (-b,-a). On which​ line does the centre of the circle lie?

Answer 1

hello friends here is your answer ,

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the circumcentre of these three points , is always the center of the circle .

thus , formula for circumcenter's coordinates is as follows :
that's for x axis
$x = \frac{x1 + x2 + x3}{3}$
thus ,
$x = \frac{0 + a - b}{3} = \frac{a - b}{3}$
for y coordinate

$y = \frac{y1 + y2 + y3 }{3} = \frac{b - a}{3}$
according to the coordinates of point , the center neither lies on x axis nor on y axis

here ,
x+y = 0
so , it lies on line x+y=0

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