If a circle passes through the point `(0,0),(a ,0)a n d(0, b)` , then find its center.

Options

A. `(b,a)`
B. `(a,b)`
C. `(a / 2, b / 2)`
D. none of the above

Answer

`(a / 2, b / 2)`

Explanation

The equation of a circle having centre `(h, k)`, having radius as `r` units, is `(x-h)^(2)+(y-k)^(2)=r^(2)`

Putting the values of given coordinates in the above expression,

Firstly take `(0,0)`

`(0-h)^(2)+(0-k)^(2)=r^(2)`

`h^(2)+k^(2)=r^(2)`

Then take`(a, 0)`

`(a-h)^(2)+(0-k)^(2)=r^(2)`

`a^(2)+h^(2)-2 a h+k^(2)=r^(2)……….(1)`

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