Q9 of 23 Page 230

What is the equation of the circle in the picture below?

The X and Y axis meets the circle at point O


The line joining the two points (0,2) and (4,0) forms the diameter of the circle.


Let the centre of the circle be C(x, y)


Using Section Formula for mid points



⇒ C(x) = 2



⇒ C(y) = 1


The coordinate of Center is (2, 1)


Radius of Circle = √((4 - 2)2 + (0 - 1)2)


⇒ Radius = √5 units


So the equation of circle is:


(x - 2)2 + (y - 1)2 = 5


⇒ x2 + y2 - 4x - 2y + 5 = 5


x2 + y2 - 4x - 2y = 0


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