Grade 11Algebra

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

Sayani

8 Years agoGrade 11

2 Answers

Arun

Approved Tutor Answer8 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

Approved Tutor Answer8 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