Answer:
2)  C.  (x - 3)² + (y + 2)² = 25
5)   x² +  y² - 8x - 16y + 54 = 0
6)   x² + y²  - 10x - 12y + 36  = 0
Explanation:
2)
center of circle = 3, -2
                             x1, y1
end point of circle = 7, 1
                                  x2, y2
  
the equation of a circle is Pythagorean theorem
x² + y² = r²    (where r is the radius of a circle)
distance between points  
(x2 - x1)² + (y2 - y1)² = r²
(7 - 3)² + (1 - (-2))² = r²
r² = 25
therefore the equation to the circle is
(x - 3)² + (y + 2)² = 25
=========================================
5)
write the general form of a circle with the center (4,8)
and containing the point (-1, 7)
distance between points  
(x2 - x1)² + (y2 - y1)² = r²
(-1 - 4)² + (7 - 8)² = r²
r² = 26
(x - 4)² + (y - 8)² = 26
(x - 4)(x - 4) +  (y - 8)(y - 8) = 26
x² - 8x + 16 + y² - 16y + 64 -26 = 0
x² +  y² - 8x - 16y + 54 = 0
=========================================
6)
find the general form of a circle with center (5,6)
and tangent to the y-axis.
            
center (5,6)
            h, k
radius = r²
r = 5
(x - h)² + (y - k)² = r²
(x - r)² + (y - k)² = r²
(x - 5)(x - 5) + (y - 6)(y - 6) = r²
x² - 10x + 25 + y² - 12y + 36 = 25
x² + y²  - 10x - 12y + 36  = 0
=========================================