Find the equation of the circle which touches both the positive axes and its centre lies on the line 6x + y = 14.

Solution:
In the given circle,
The circle touches positive x-axis and positive y-axis.
Let the co-ordinates of the centre of the circle be represented by (h,k).
Let the radius of the circle be represented by r.
In such case, r = h = k.

Given,
Centre lies on the line 6x + y = 14
or, 6h + k = 14
or, 6h + h = 14
or, 7h = 14
So, h = 2

So, r = h = k = 2 units.

Now, equation of circle is given by,

(x - h)² + (y - k)² = r²
or, (x - 2)² + (y - 2)² = 2²
or, (x² - 4x +4) + (y² - 4y +4) = 4
or, x² + y² - 4x - 4y + 4 = 0 is the required equation.

Hence, the required equation of the given circle is x² + y² - 4x - 4y + 4 = 0.