Question 535695
Starting with the general form for a circle with center at (h, k) and radius, r.
{{{(x-h)^2+(y-k)^2 = r^2}}}
The center is given as (3, 4) so substitute h = 3 and k = 4.
{{{(x-3)^2+(y-4)^2 = r^2}}}
To find the radius r, the distance from the center to the circumference, you know that the circumference touches the line x = 6, so the radius would be the distance from the center (x = 3) to the line (x = 6) which gives you a radius of 6-3 = 3. Now you can complete the equation:
{{{(x-3)^2+(y-4)^2 = 3^2}}} or
{{{highlight((x-3)^2+(y-4)^2 = 9)}}}
The graph:
{{{graph(400,400,-5,10,-5,10,sqrt(9-(x-3)^2)+4,-sqrt(9-(x-3)^2)+4)}}}