Question

How do you find the equation of a circle with centre (5,4) and just touches the x-axis?

Answer 1

The equation of a circle with centre in `(a,b)` and radius `r` is `(x-a)^2+(y-b^2)=r^2`

Explanation:

We know that the centre is `(a,b)=(5,4)`, so we only need to find out the radius. But the circle 'just touches' the x-axis, so the distance of the centre to the x-axis is 4 (see the figure):

graph{(x-5)^2+(y-4)^2=16 [-5.79, 14.21, -1.16, 8.84]}

Then the radius is 4, and the equation is:

`(x-5)^2+(y-4)^2=16`