Find the equation of a circle which passes through the origin and whose centre is (a, b).

Explanation

Centre of circle C(h, k) = (a, b)
Radius of circle `r = OC`
`= sqrt((a-0)^(2)+(b-0)^(2))`
`=sqrt(a^(2)+b^(2))`
`:.` Equation of circle
`(x-h)^(2)+(y-k)^(2)=r^(2)`
`rArr(x-a)^(2)+(y-b)^(2)=(sqrt(a^(2)+b^(2)))^(2)`
`rArr x^(2) -2ax +a^(2) +y^(2)-2by +b^(2)=a^(2)+b^(2)`
`rArr x^(2)+y^(2)-2ax - 2by =0`.