MHB What is the equation of the circle tangent to the x-axis and with center (3, 5)?

[mathdad]

Find the equation of the circle tangent to the x-axis and with center (3, 5).

Can someone provide the steps needed to solve this problem?

 

[MarkFL]

The equation of a circle centered ar $(h,k)$ is given by:

$$(x-h)^2+(y-k)^2=r^2$$

If the circle is tangent to the $x$-axis, then its radius must be $r=|k|\implies r^2=k^2$, thus we have:

$$(x-h)^2+(y-k)^2=k^2$$

We are given $(h,k)=(3,5)$, so plug in those numbers. :D

 

[mathdad]

The equation of a circle centered ar $(h,k)$ is given by:

$$(x-h)^2+(y-k)^2=r^2$$

If the circle is tangent to the $x$-axis, then its radius must be $r=|k|\implies r^2=k^2$, thus we have:

$$(x-h)^2+(y-k)^2=k^2$$

We are given $(h,k)=(3,5)$, so plug in those numbers. :D

(x - h)^2 + (y - k)^2 = k^2

(x - 3)^2 + (y - 5)^2 = 5^2

(x - 3)^2 + (y - 5)^2 = 25