Write the equation in standard form for the circle with center (4,0) passing through 4,(11/2).

Answer:The standard equation of circle is  [tex](x-4)^2 + (y)^2  = (\frac{11}{2}) ^2[/tex]Step-by-step explanation:The given circle has Center  = (4,0)Passing through (4,11/2)The standard form of the Circle is given as:[tex](x-h)^2 + (y-k)^2  = r^2[/tex]Here, (h,k) is the center coordinates and r : radius of the given circle.So, here according to the question:(h,k) = (4,0)  , (x,y) = (4,11/2)Putting the above value sin the equation of circle, determine the value of r:[tex](4-4)^2 + (\frac{11}{2} -0)^2  = r^2\\\implies (\frac{11}{2}) ^2 = r^2\\\implies r = (\frac{11}{2})[/tex]Hence, the standard equation of circle is  [tex](x-4)^2 + (y-0)^2  = (\frac{11}{2}) ^2[/tex]