If a circle passes through the point (0, 0),(*a*, 0),(0, *b*) then find the coordinates of its centre.

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#### Solution

The general equation of the circle is *x*^{2} + *y*^{2} + 2*gx* + 2*fy *+ *c* =^{ }0

Now, it is passing through (0, 0)

∴ *c* = 0

Also, it is passing through (*a*, 0)

∴ *a*^{2} + 2*ag* =^{ }0

⇒ *a*(*a* + 2*g*) = 0

⇒*a* + 2*g* = 0

\[\Rightarrow g = - \frac{a}{2}\]

Again, it is passing through (0, *b*)

∴* **b*^{2} + 2*bf* =^{ }0

⇒ *b*(*b* + 2*f*) = 0

⇒*b* + 2*f* = 0

\[\Rightarrow f = - \frac{b}{2}\]

The coordinates of its centre are given by

\[\left( - g, - f \right) = \left( \frac{a}{2}, \frac{b}{2} \right)\]

Concept: Circle - Standard Equation of a Circle

Is there an error in this question or solution?

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