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I will not solve the entire assignment for you, but will give you enough information to get you started, in accordance with enotes policies.
The equation of the circle is given as (x-a)^2 + (y-b)^2 = r^2
where the center of the circle is at coordinates (a,b) and the radius of the circle is r.
So for using the question #1 of your assignment as an example, the given equation is
(x-4)^2 + (y-2)^2 = 25
comparing this equation with the standard equation of circle, we get the center as (4,2) and the radius = (25)^(1/2) = 5 (we will disregard the other root -5, as that is not possible for radius of a circle). Using this information, you can draw the circle. Any points on the circle can be determined by as the set that satisfies the above equation. The simplest points on the circle can correspond to either x=0 or y=0 to determine the x and y intercepts.
You can solve questions 1-3 using this example.
For questions, 4 and 5, given the location of center and radius, we can determine the equation of circle.
For examples, Q 4: center is at (4,0) and radius = 3, the equation (comparing with standard equation) is given as:
(x-4)^2 + (y-0)^2 = 3^2 or (x-4)^2 + y^2 = 9
and the circle can be plotted by finding the intercepts of the circle.
Hope this helps.
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