Question

A circle is centered at (3, 8) and is tangent to the x-axis. Write its equation in standard form.

Answer 1

The radius of the circle is: r = 8 

(x - 3)^2 + (y - 8)^2 = 8^2

(x - 3)^2 + (y - 8)^2 = 64.

Answer 2

Answer:

$(x-3)^2+(y-8)^2=64$

Step-by-step explanation:

We have been given that a circle is centered at (3, 8) and is tangent to the x-axis.

We know that the equation of  a circle in standard form is in format: $(x-h)^2+(y-k)^2=r^2$, where,

$(h,k)$= Coordinates of center of circle,

$r$= Radius of circle.

Since x-axis is tangent to our given circle, so the radius of our circle will be 8 units as the radius of a circle is segment that connects the center of a circle with its perimeter. Since y-coordinate of our center is 8, this means the radius of circle is 8 units from the tangent line that is x-axis.

Upon substituting our given values in standard form of circle we will get,

$(x-3)^2+(y-8)^2=8^2$

$(x-3)^2+(y-8)^2=64$

Therefore, the equation of our given circle in standard form would be $(x-3)^2+(y-8)^2=64$.