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find the radius of the circle which passes through the origin and the points (a,0) and (0,b)

find the radius of the circle which passes through the origin and the points (a,0) and (0,b)

Grade:11

2 Answers

Arun
25750 Points
6 years ago
Dear student
 
let the equation of circle :
x2 + y2 + 2gx+ 2fy + c = 0
now pass it from (0, 0):
c= 0
 
now pass it from (a, 0)
a2 + 2ag = 0
g = – a/2
 
now pass it from (0, b)
b2 + 2fb = 0
f = – b/2
 
now radius of circle = \sqrt(g2 + f2 –c)
 = \sqrt(a2 + b2)/4
 = ½ \sqrt(a2 + b2)
 
Regards
Arun (askIITians forum expert)
Meet
137 Points
6 years ago
Let the equation of the circle is x^2+y^2+2gx+2fy+c=0 so if it passes through the origin then c=0, if it passes through (a,0) then a^2+2ga=0 , if passes through (0,b) then b^2+2bf=0 so the equation of circle is x^2+y^2-ax-by=0 so therefore radius of the circle is √(a^2+b^2)/4

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