A circle A has equation x^2+y^2-6x-14y+54=0. Find a) the coordinates of the centre of A, b) the radius of the circle A.

The standard equation of a circle is in the form (x-a)^2+(y-b)^2=r^2, where the coordinates of the centre of the circle is (a,b) and the radius of the circle is r. Therefore, you must put the given equation into the standard form by completing the square for the expresions x^2-6x and y^2-14y in order to find the centre and radius if the circle.When you have completed the square for the two expressions, the equation will be (x-3)^2-9+(y-7)^2-49+54=0. To get the equation into the standard form you must then simplify and rearrange the equation to get (x-3)^2+(y-7)^2=4. Therefore, the coordinates of the centre of the circle A is (3,7) and the radius of the circle A is 2.