Respuesta :
The equation of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h,k) is the center of the circle and r the radius. In this case we know the center (3,4) 1*but we don't know the radius, then we have to find it first.
To find the radius we need to use the fact that the circle is tangent to the x-axis. We know that the distance from a point (h,k) to a line Ax+By+C=0 is given by:
[tex]d=\frac{\lvert Ah+Bk+C\rvert}{\sqrt[]{A^2+B^2}}[/tex]Now, the x axis has equation y=0; this means that A=0, B=1 and C=0. then we have:
[tex]d=\frac{\lvert1\cdot4\rvert}{\sqrt[]{1^2^{}}}=\frac{4}{1}=4[/tex]This means that the radius is 4.
Once we have the radius we plug its value and the value of the center in the equation, then:
[tex](x-3)^2+(y-4)^2=4^2[/tex]Therefore, the equation is:
[tex](x-3)^2+(y-4)^2=16[/tex]