A circle cuts the x-axis at (4,0) and (14,0), and cuts the y-axis at (0,6) and (0,8). Find it's equation

It is not a circle but you can find the equation of the ellipse.

To do this we need to work out the major and minor radii and the centre

The centre is at (9, 7)

The major (y) radius is 1 and the minor (x) radius is 5

Therefore the equation is (x-9) / 5 + (y-7) / 1 = 1