The general equation of a circle is:
r^2 = (x-x_o)^2 + (y-y_o)^2
where:
r is the radius
x_o is the x-coordinate of the origin
y_o is the y-coordinate of the origin
The equation becomes:
r^2 = (x--5)^2 + (y-4)^2
r^2 = (x+5)^2 + (y-4)^2
Note that since it is -x_o we did - - 5, and it turned it into a +5. Pay attention to the signs.
What remains to be found is r.
The x-axis as the equation y=0, therefore the line perpendicular to this that will hit the center of the circle will have to be x=k. Since we know the center of the circle has the x-coordinate -5, then the line that hits the center of the circle will be at x=-5. The point of that line that intersects the x-axis is (-5,0). The radius is the distance between the center of the circle and this point, so:
r = sqrt((-5--5)^2 + (4-0)^2)
r = sqrt(0+4^2)
r = sqrt(4^2)
r = 4
Our final equation is:
16 = (x+5)^2 + (y-4)^2
We can verify that (-5,0) is on the circle:
16 = (-5+5)^2+(0-4)^2
16 = 0^2 + (-4)^2
16 = 0 + 16
16 = 16
Here's a graphical rendition of the circle:
https://www.desmos.com/calculator/xizwgbgksu
