Find the equation of the circle which lies in the first quadrant and touching each-co ordinate-axis at a distance of 2 units from the origin.

Explanation

The circle is touching the co-ordinate axes.

`rArr` Both the x-axis and y-axis are tangents to the circle.
`therefore` The perpendicular distance from the centre to the point of contact of the circle and the co-ordinate axes in the radius of the circle.
Since the point of contact is 2 units away from the centre.
`therefore` Radius = 2 units and centre = (2, 2)
`therefore` The required equation of the circle is given by `(x-h)^(2) + (y-k)^(2) = r^(2)`
i.e., `(x-2)^(2) + (y-2)^(2) = (2)^(2)`