Question

If a circle passes through the point (0, 0), (a, 0) and (0, b) then

the coordinate of its centre is____.

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Answer 1

Answer:

Co-ordinates for the center will be $\left(\dfrac{a}{2},\dfrac{b}{2}\right)$

Step-by-step explanation:

It is given that the circle passes through the points $(0,0)$ ; $(a,0)$ and $(0,b)$

Only one unique circle can go through 3 distinct points if they don't lie in a straight line.

The center for this unique circle lies on the intersection of the perpendicular bisector of all 3 sides.

$(0,0)$ lies on origin.
$(a,0)$ will lie on x-axis since it's 'y' co-ordinate is zero.
$(0,b)$ will lie on y-axis since it's 'x' co-ordinate is zero.

The perpendicular bisector of the line formed by joining (0,0) and (a,0) will be represented by $x=\dfrac{a}{2}$

The perpendicular bisector of the line formed by joining (0,0) and (a,0) will be represented by $y=\dfrac{b}{2}$

These two lines will intersect at the point $\left(\dfrac{a}{2},\dfrac{b}{2}\right)$ which coincides with the center of the required circle.

Therefore, the co-ordinates of the center are $\left(\dfrac{a}{2},\dfrac{b}{2}\right)$