Q. 15

Find the equation of a circle passing through the origin and intercepting lengths a and b on the axes.

Answer :

From the figure

AD = b units and AE = a units.


D(0, b), E(a, 0) and A(0, 0) lies on the circle. C is the centre.



The general equation of a circle: (x - h)2 + (y - k)2 = r2


…(i), where (h, k) is the centre and r is the radius.


Putting A(0, 0) in (i)


(0 - h)2 + (0 - k)2 = r2


h2 + k2 = r2 …(ii)


Similarly putting D(0, b) in (i)


(0 - h)2 + (b - k)2 = r2


h2 + k2 + b2 - 2kb = r2


r2 + b2 - 2kb = r2


b2 - 2kb = 0


(b- 2k)b = 0


Either b = 0ork =


Similarly putting E(a, 0) in (i)


(a - h)2 + (0 - k)2 = r2


h2 + k2 + a2 - 2ha = r2


r2 + a2 - 2ha = r2


a2 - 2ha = 0


(a- 2h)a = 0


Either a = 0orh =


Centre = C


r2 = h2 + k2



Putting the value of r2 , h and k in equation (i)


(x - h)2 + (y - k)2 = r2





which is the required equation.


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