Question

How do you find the equation of a circle if the centre of the circle is (5,13) and touches the x axis?

Answer 1

`(x-5)^2+(y-13)^2=13^2`

Explanation:

The general equation for a circle with center `(color(red)(a),color(blue)(b))` and radius `color(green)(r)` is
`color(white)("XXX")(x-color(red)(a))^2+(y-color(blue)(b))^2= color(green)(r)^2`

If the center of the center of a circle is at `(color(red)(5),color(blue)(13))` and it is tangent to the X-axis
then its radius is the distance from the center to the X-axis,
i.e. the `y` coordinate of its center (in this case `color(green)(13)`)