Question

How do you find the equation of the circle with centre (2,5) which touches the x axis?

Answer 1

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

Explanation:

The general form for the equation of a circle is:
`color(white)("XXX")(x-x_c)^2+(y-y_c)^2=r^2`
where `(x_c,y_c)` is the center of the circle
and `r` is the circle's radius.

We are told that `(x_c,y_c)=(2,5)`
and that the circle touches the x-axis.
`rarr` the distance from the center of the circle to the x-axis is `y_c`
`rarr` the radius `r=y_c=5`

Substituting
`color(white)("XXX")2rarr x_c`,
`color(white)("XXX")5rarry_c`, and
`color(white)("XXX")5rarrr`
in the general equation:
`color(white)("XXX")(x-2)^2+(y-5)^2=5^2`